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Published on November 8, 2019 by Rebecca Bevans . Revised on June 22, 2023.
Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics . It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.
There are 5 main steps in hypothesis testing:
Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps.
Step 1: state your null and alternate hypothesis, step 2: collect data, step 3: perform a statistical test, step 4: decide whether to reject or fail to reject your null hypothesis, step 5: present your findings, other interesting articles, frequently asked questions about hypothesis testing.
After developing your initial research hypothesis (the prediction that you want to investigate), it is important to restate it as a null (H o ) and alternate (H a ) hypothesis so that you can test it mathematically.
The alternate hypothesis is usually your initial hypothesis that predicts a relationship between variables. The null hypothesis is a prediction of no relationship between the variables you are interested in.
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For a statistical test to be valid , it is important to perform sampling and collect data in a way that is designed to test your hypothesis. If your data are not representative, then you cannot make statistical inferences about the population you are interested in.
There are a variety of statistical tests available, but they are all based on the comparison of within-group variance (how spread out the data is within a category) versus between-group variance (how different the categories are from one another).
If the between-group variance is large enough that there is little or no overlap between groups, then your statistical test will reflect that by showing a low p -value . This means it is unlikely that the differences between these groups came about by chance.
Alternatively, if there is high within-group variance and low between-group variance, then your statistical test will reflect that with a high p -value. This means it is likely that any difference you measure between groups is due to chance.
Your choice of statistical test will be based on the type of variables and the level of measurement of your collected data .
Based on the outcome of your statistical test, you will have to decide whether to reject or fail to reject your null hypothesis.
In most cases you will use the p -value generated by your statistical test to guide your decision. And in most cases, your predetermined level of significance for rejecting the null hypothesis will be 0.05 – that is, when there is a less than 5% chance that you would see these results if the null hypothesis were true.
In some cases, researchers choose a more conservative level of significance, such as 0.01 (1%). This minimizes the risk of incorrectly rejecting the null hypothesis ( Type I error ).
The results of hypothesis testing will be presented in the results and discussion sections of your research paper , dissertation or thesis .
In the results section you should give a brief summary of the data and a summary of the results of your statistical test (for example, the estimated difference between group means and associated p -value). In the discussion , you can discuss whether your initial hypothesis was supported by your results or not.
In the formal language of hypothesis testing, we talk about rejecting or failing to reject the null hypothesis. You will probably be asked to do this in your statistics assignments.
However, when presenting research results in academic papers we rarely talk this way. Instead, we go back to our alternate hypothesis (in this case, the hypothesis that men are on average taller than women) and state whether the result of our test did or did not support the alternate hypothesis.
If your null hypothesis was rejected, this result is interpreted as “supported the alternate hypothesis.”
These are superficial differences; you can see that they mean the same thing.
You might notice that we don’t say that we reject or fail to reject the alternate hypothesis . This is because hypothesis testing is not designed to prove or disprove anything. It is only designed to test whether a pattern we measure could have arisen spuriously, or by chance.
If we reject the null hypothesis based on our research (i.e., we find that it is unlikely that the pattern arose by chance), then we can say our test lends support to our hypothesis . But if the pattern does not pass our decision rule, meaning that it could have arisen by chance, then we say the test is inconsistent with our hypothesis .
If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.
Methodology
Research bias
Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.
A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.
A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).
Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.
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Hypothesis is a testable statement that explains what is happening or observed. It proposes the relation between the various participating variables. Hypothesis is also called Theory, Thesis, Guess, Assumption, or Suggestion. Hypothesis creates a structure that guides the search for knowledge.
In this article, we will learn what is hypothesis, its characteristics, types, and examples. We will also learn how hypothesis helps in scientific research.
Table of Content
Hypothesis meaning, characteristics of hypothesis, sources of hypothesis, types of hypothesis, simple hypothesis, complex hypothesis, directional hypothesis, non-directional hypothesis, null hypothesis (h0), alternative hypothesis (h1 or ha), statistical hypothesis, research hypothesis, associative hypothesis, causal hypothesis, hypothesis examples, simple hypothesis example, complex hypothesis example, directional hypothesis example, non-directional hypothesis example, alternative hypothesis (ha), functions of hypothesis, how hypothesis help in scientific research.
A hypothesis is a suggested idea or plan that has little proof, meant to lead to more study. It’s mainly a smart guess or suggested answer to a problem that can be checked through study and trial. In science work, we make guesses called hypotheses to try and figure out what will happen in tests or watching. These are not sure things but rather ideas that can be proved or disproved based on real-life proofs. A good theory is clear and can be tested and found wrong if the proof doesn’t support it.
A hypothesis is a proposed statement that is testable and is given for something that happens or observed.
Here are some key characteristics of a hypothesis:
Hypotheses can come from different places based on what you’re studying and the kind of research. Here are some common sources from which hypotheses may originate:
Here are some common types of hypotheses:
Simple Hypothesis guesses a connection between two things. It says that there is a connection or difference between variables, but it doesn’t tell us which way the relationship goes.
Complex Hypothesis tells us what will happen when more than two things are connected. It looks at how different things interact and may be linked together.
Directional Hypothesis says how one thing is related to another. For example, it guesses that one thing will help or hurt another thing.
Non-Directional Hypothesis are the one that don’t say how the relationship between things will be. They just say that there is a connection, without telling which way it goes.
Null hypothesis is a statement that says there’s no connection or difference between different things. It implies that any seen impacts are because of luck or random changes in the information.
Alternative Hypothesis is different from the null hypothesis and shows that there’s a big connection or gap between variables. Scientists want to say no to the null hypothesis and choose the alternative one.
Statistical Hypotheis are used in math testing and include making ideas about what groups or bits of them look like. You aim to get information or test certain things using these top-level, common words only.
Research Hypothesis comes from the research question and tells what link is expected between things or factors. It leads the study and chooses where to look more closely.
Associative Hypotheis guesses that there is a link or connection between things without really saying it caused them. It means that when one thing changes, it is connected to another thing changing.
Causal Hypothesis are different from other ideas because they say that one thing causes another. This means there’s a cause and effect relationship between variables involved in the situation. They say that when one thing changes, it directly makes another thing change.
Following are the examples of hypotheses based on their types:
Hypotheses have many important jobs in the process of scientific research. Here are the key functions of hypotheses:
Researchers use hypotheses to put down their thoughts directing how the experiment would take place. Following are the steps that are involved in the scientific method:
Mathematics Maths Formulas Branches of Mathematics
A hypothesis is a testable statement serving as an initial explanation for phenomena, based on observations, theories, or existing knowledge. It acts as a guiding light for scientific research, proposing potential relationships between variables that can be empirically tested through experiments and observations.
The hypothesis must be specific, testable, falsifiable, and grounded in prior research or observation, laying out a predictive, if-then scenario that details a cause-and-effect relationship. It originates from various sources including existing theories, observations, previous research, and even personal curiosity, leading to different types, such as simple, complex, directional, non-directional, null, and alternative hypotheses, each serving distinct roles in research methodology .
The hypothesis not only guides the research process by shaping objectives and designing experiments but also facilitates objective analysis and interpretation of data , ultimately driving scientific progress through a cycle of testing, validation, and refinement.
What is a hypothesis.
A guess is a possible explanation or forecast that can be checked by doing research and experiments.
The components of a Hypothesis are Independent Variable, Dependent Variable, Relationship between Variables, Directionality etc.
Testability, Falsifiability, Clarity and Precision, Relevance are some parameters that makes a Good Hypothesis
You cannot prove conclusively that most hypotheses are true because it’s generally impossible to examine all possible cases for exceptions that would disprove them.
Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data
Yes, you can change or improve your ideas based on new information discovered during the research process.
Hypotheses are used to support scientific research and bring about advancements in knowledge.
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We have heard of many hypotheses which have led to great inventions in science. Assumptions that are made on the basis of some evidence are known as hypotheses. In this article, let us learn in detail about the hypothesis and the type of hypothesis with examples.
A hypothesis is an assumption that is made based on some evidence. This is the initial point of any investigation that translates the research questions into predictions. It includes components like variables, population and the relation between the variables. A research hypothesis is a hypothesis that is used to test the relationship between two or more variables.
Following are the characteristics of the hypothesis:
Following are the sources of hypothesis:
There are six forms of hypothesis and they are:
It shows a relationship between one dependent variable and a single independent variable. For example – If you eat more vegetables, you will lose weight faster. Here, eating more vegetables is an independent variable, while losing weight is the dependent variable.
It shows the relationship between two or more dependent variables and two or more independent variables. Eating more vegetables and fruits leads to weight loss, glowing skin, and reduces the risk of many diseases such as heart disease.
It shows how a researcher is intellectual and committed to a particular outcome. The relationship between the variables can also predict its nature. For example- children aged four years eating proper food over a five-year period are having higher IQ levels than children not having a proper meal. This shows the effect and direction of the effect.
It is used when there is no theory involved. It is a statement that a relationship exists between two variables, without predicting the exact nature (direction) of the relationship.
It provides a statement which is contrary to the hypothesis. It’s a negative statement, and there is no relationship between independent and dependent variables. The symbol is denoted by “H O ”.
Associative hypothesis occurs when there is a change in one variable resulting in a change in the other variable. Whereas, the causal hypothesis proposes a cause and effect interaction between two or more variables.
Following are the examples of hypotheses based on their types:
Following are the functions performed by the hypothesis:
Researchers use hypotheses to put down their thoughts directing how the experiment would take place. Following are the steps that are involved in the scientific method:
What is hypothesis.
A hypothesis is an assumption made based on some evidence.
What are the types of hypothesis.
Types of hypothesis are:
Define complex hypothesis..
A complex hypothesis shows the relationship between two or more dependent variables and two or more independent variables.
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One Variable Hypothesis Testing
Learning Objectives
In this section, we will step through several examples of how to perform hypothesis testing for sample means. Let us start by recapping the required formula presented in the previous section :
H 0 : [latex]\mu = \mu_{original}[/latex] (all tails)
H A : [latex]\mu \mu_{original}[/latex] (right-tailed), [latex]\mu \neq \mu_{original}[/latex] (two-tailed)
The test statistic formula is the same, regardless of what tailed test we are performing:
\[t_{test} = \frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}\]
We could use Excel’s T.DIST() function to calculate all p-values but, it is slightly easier to use different functions depending on which hypothesis test we are performing (left, right or two-tailed):
\[p_{\text{ left-tailed}}=\text{T.DIST}(t_{test},n-1,\text{TRUE})\]
\[p_{\text{ two-tailed}}=\text{T.DIST.2T}(\text{abs}(t_{test}), n-1) \]
\[p_{\text{ right-tailed}}=\text{T.DIST.RT}(t_{test},n-1)\]
Remember: When use T.DIST.2T , we must only input a positive t[latex]_{test}[/latex] value. For this reason, we can use an absolute value call ABS() to ensure that we input a positive value in the T.DIST.2T function.
Let us start by working through a right-tailed hypothesis test problem for a sample with one mean.
Problem Setup : Stats Canada has published a report stating that the average starting business student’s starting salary is $5,400 per month. Your college’s marketing team believes that their business diploma grads earn higher than $5,400, on average, upon graduation. A sample of 100 grads is polled and their starting salaries are reported. The average starting salary is reported at $6,500 with a standard deviation of $3,200.
Question : Is there sufficient evidence, based on the sample of 100 grads to support the marketing team’s hypothesis at a 5% level of significance?
You Try : Scroll through the questions below to solve the hypothesis test problem above.
Solutions : Click here to download the Excel solutions and click on the sections below to reveal the written solutions to each part of the above exercise.
We want to prove that the mean income after graduation is higher than $5,400. For this reason, we need our sample result to be significantly higher than $5,400. The rejection region would be the upper 5% right tail. The original mean of $5,400 is what we are comparing to and is marked in the middle of the graph.
This is a right-tailed test. In order to prove that the mean starting salary is higher than $5,400, we will need our sample result to be far enough above the original mean of $5,400 and be, therefore, in the upper right tail (upper rejection region).
[latex]\begin{align} t_{test} &= \frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}} \\ &= \frac{\$6,500-\$5,400}{\frac{\$3,200}{\sqrt{100}}} \\ &= 3.4375 \end{align}[/latex]
Because we are performing a right-tailed test on a mean, we will use Excel’s T.DIST.RT(t test , n-1) function:
[latex]p\text{-value}=\text{T.DIST.RT}(3.4375, 99) = 0.00043[/latex]
Because the p-value = 0.00043 (0.043%) is less than (<) the level of significance of 5% (0.05), we reject H 0 .
Because we rejected H 0 , there is sufficient evidence to conclude that the college’s business diploma grads earn higher than $5,400 upon graduation.
In this example, we will perform a two-tailed hypothesis test for a sample with one mean. We will return to our example of quality control for space fasteners that could be supplied to organizations and companies like NASA , SpaceX and other companies that build satellites and other machines used in space.
Problem Setup: A company supplies Standard Hexagon Head Cap Screws. They perform regular quality control checks. In this case, they are performing quality control on their 5/8 inch standard hexagon head cap screws.
Question : At the 1% level of significance, is there sufficient evidence to conclude that this batch of hexagon head cap screws are not actually 5/8 inches in length?
We want to prove that (or check if) the average screw length from this batch of screws is not 5/8 inches = 0.625 inches in length. When proving that the screws are not equal to 0.625 inches, we could prove this by having a batch of screws with an average length much longer or much shorter than 0.625 inches. For this reason, extreme values in either tail would prove this. This means we have a two-tailed problem:
This is a two-tailed test, as described in the previous section. We always have a two-tailed test when the alternate hypothesis (H A ) contains a ‘not equal’ (≠) symbol.
[latex]\begin{align} t_{test} &= \frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}} \\ &= \frac{0.6245-0.625}{\frac{0.0124}{\sqrt{100}}} \\ &= -0.4032 \end{align}[/latex]
[latex]p\text{-value}=\text{T.DIST.2T}(abs(-0.4032), 99) = 0.68765[/latex]
Because the p-value = 0.68765 (68.765%) is more than (>) the level of significance of 1% (0.01), we do not reject H 0 .
Because we failed to reject H 0 , there is not sufficient evidence to conclude that the batch of hexagon head cap screws do not have an average length of 5/8 inches.
In this example, we will perform a left-tailed hypothesis test for a sample with one mean.
Problem Setup : A salesman claims that his product, XYZ tires, will last at least 100,000 kilometers without failure. Your company is considering using such tires in its customized Jeeps that it manufactures however you are skeptical of the salesman’s claim. Through some laborious research you receive some information from an independent source regarding the life expectancy of XYZ tires. The independent source provides the following information on 100 randomly selected tires: the sample of tires has a mean life of 98,000 km with a standard deviation of 9,434 km.
Question : Is there sufficient evidence, at the 5% level of significance, to conclude that the salesmen’s claim regarding the life expectancy of XYZ tires is an exaggeration?
Solutions : Click here to download the Excel solutions to the above problem and click on the sections below to reveal the written solutions to each part of the above exercise.
We want to prove that the average number of kilometers the tires will last is less than 100,000 kilometers (km). If the sample of 100 tires last much less than 100,000 km, there is sufficient evidence to conclude that the real average duration of the tires is less than 100,000 km. This means we need a result in the left-tail or far below 100,000.
This is a left-tailed test. In order to prove that the mean number of kilometers that tires last is lower than 100,000 km, we will need our sample result to be far enough below the stated mean of 100,000 and be, therefore, in the lower left tail.
[latex]\begin{align} t_{test} &= \frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}} \\ &= \frac{98,000-100,000}{\frac{9,434}{\sqrt{100}}} \\ &= -2.1200 \end{align}[/latex]
Because we are performing a left-tailed test on a mean, we will use Excel’s T.DIST(t test , n-1, TRUE) function:
[latex]p\text{-value}=\text{T.DIST}(-2.12, 99, \text{TRUE}) = 0.01825[/latex]
Because the p-value = 0.01825 (1.825%) is less than (<) the level of significance of 5% (0.05), we reject H 0 .
Because we rejected H 0 , there is sufficient evidence to conclude that the salesmen’s claim regarding the life expectancy of XYZ tires is an exaggeration.
An Introduction to Business Statistics for Analytics (1st Edition) Copyright © 2024 by Amy Goldlist; Charles Chan; Leslie Major; Michael Johnson is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License , except where otherwise noted.
The appropriate way to state the conclusion of the given statement is:
The results of the statistical test suggest that women have a shorter mean nose length than men (p = 0.04, α = 0.05).
A null hypothesis is that the mean nose lengths of men and women are the same.
The alternative hypothesis is that women have a shorter mean nose length than men.
Alpha for the problem is.05.
A statistical test is done and the p-value is 0.04.
Hence based on the condition we frame it as:
Hence we get the required answer,
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A piece of granite is being cut for a building foundation. You want its length to be six times its height and its width to be four times its height. If you want the granite to be 1,536 cubic centimeters, what will its length, width, and height be? Use x for the height of the granite
For the given volume of the granite is 1,536 cubic centimeters then as per given relation between dimensions the length , width , and height of the granite is equal to 24cm , 16cm , 4cm respectively.
As given in the question,
Given volume of the granite = 1,536 cubic centimeters
Let us consider 'x' be the height of the granite
As per given relation between dimensions we have,
length of the granite = 6x
Width of the granite = 4x
Volume of the granite = length × width × height
⇒ 1,536 = 6x × 4x × x
⇒ 24x³ = 1,536
⇒ x³ = 1,536 / 24
Height = 4cm
Length = 6 × 4
= 24cm
Width = 4 × 4
= 16cm
Therefore, for the given volume of the granite is 1,536 cubic centimeters then as per given relation between dimensions the length , width , and height of the granite is equal to 24cm , 16cm , 4cm respectively.
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Given f(x) = -8x3+2x2+5x and g(x) = -2x+6-6x3, find f(x) - g(x) Please help
[tex](-8x^3+2x^2+5x)-(-6x^3-2x+6) \\ \\ =-8x^3+2x^2+5x+6x^3+2x-6 \\ \\ =\boxed{-2x^3 +2x^2+7x-6}[/tex]
a student is working full-time (at least 40 hours a week) and is also starting their first semester of college. this student wants to maintain a high gpa and graduate as soon as possible. how many credits hours should the student take? group of answer choices no more than 16-credit hours no more than 13-credit hours no more than 10-credit hours no more than 7-credit hours
The correction option would be no more than 7- credit hours
Maintaining focus and diligence throughout the course of the program is necessary for a student to graduate with a high GPA and a timeline that is not excessively long. Students should only enroll in a maximum of 7 credits in order to graduate successfully.
In order to improve focus and create a good time for studying, the student should take as few credit hours as possible.
Typically, students take no more than six hours of credit total per semester. The nearest choice would therefore be no more than 7, as that is the limit.
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Phil and Meredith work for a book publisher editing mathematics textbooks. Phil has less experience and takes twice as long as Meredith to edit a textbook. Together, it takes them 6 hours to edit a textbook. How long does it take Phil to edit a textbook if he works alone? _ hours. How long does it take Meredith to edit a textbook if she works alone? _ hours
Let the time for Meredith to finish the work alone be x , then for Phil it is 2x .
In one hour Meredith edits 1/x and Phil edits 1/(2x) of the text.
Step-by-step explanation:
Let's take for a hour,
→ Phil = 1/2t
→ Meredith = 1/t
Forming the equation,
→ (1/2t) + (1/t) = 1/6
Now the value of time (t) will be,
→ (1/2t) + (2/2t) = 1/6
→ 3/2t = 1/6
→ 2t = 6 × 3
→ [ t = 9 ]
Then time for each person is,
→ Phil = 2t = 2(9) = 18 hours
→ Meredith = t = 9 hours
Hence, these are the time taken.
Help Im begging Help !!!!!!!!! pls!!!!! How many numbers less than 30 have an odd number of factors?
--------------------------------
Only the perfect squares have odd number of factors.
I need help!!! Thank you
i think 32. because have 5 slot and 40 division 5 equal 8. us have 4 slot no réd color
Describe how you could move the solid polygon to exactly match the dashed polygon using a series of two transformations.
Reflect polygon [tex]O[/tex] over the [tex]y[/tex]-axis and then translate using the vector [tex](-2, 3)[/tex].
last math question i think
since shipping company a is 7 dollars plus 0.5 per pound we write it like
And the second one is similar but it’s 11 plus 0.25 for each pound
Therefore b is the best graph
Hopes this helps
Solve the following inequality for mm. Write your answer in simplest form. 9m+5≤10m-7
1kg = 1000 g 3 oz.=85 g 11 lbs. = 5 kg 4 kg = 141 oz. Determine the approximate value of each quantity.
There are 1000 grams in a kilogram. As a result, the ratio of kilograms to grams is 1: 1000. Additionally, it implies that a kilogram and a kilogram are equivalent.
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Andrea collected data for a school project, but accidentally spilled her coffee on her page. She knows that the values represented a linear function. For this function, what is the value of y when x = 0?.
The value of Y at x=0 is 4, or 4.
A line's steepness and direction are measured by the line's slope . Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line.
The ratio of " vertical change" to "horizontal change" between two different points on a line is calculated using the slope of a line formula.
We will comprehend the slope-finding method and its applications in this article.
According to our question-
Y = mx + b is the equation of a linear function, where m is the slope, y is the dependent variable, and x is the independent variable. The equation for the linear function through the point is
Assume that the data has the points (0, 0) and (60, 30). The linear function's equation is as follows:
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side $cd$ of rectangle $abcd$ measures 12 meters, as shown. each of the three triangles with a side along segment $cd$ is an equilateral triangle. what is the total area of the shaded regions? express your answer in simplest radical form.
The area of the shaded region is 8√3 m².
Here we have to find the total area of the shaded regions.
The three triangles along CD are all equilateral and they all have the same height, so they are all congruent to each other.
The length of each side of these three triangles = 12/3
= 4m
We know that an angle along line CD between two 60° angles = 180° - 60° - 60°
= 60°
So the two shaded triangles are also equilateral triangles with a side length of 4m.
The area of shaded the region = 2× ( area of one shaded triangle)
= 2 ×( 1/2 × base × height)
= 2×( 1/2 × 4×2√3)
= 8√3 meter²
Therefore we get an area of the shaded part 8√3.
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the probability that it is friday and that a student is absent during professor pouokam class is 0.03. since there are 5 school days in a week, the probability that it is friday is 0.2. what is the probability that a student is absent given that today is friday?
The probability that a student is going to be absent given that today is Friday is 3/20.
Here in the given problem, we have been given two conditions, that is -
The probability of the student being absent during professor Pouokam's class is = A = 0.03 (i)
The probability of it being Friday is = F = 0.2 (ii)
We know that in order to solve we need to use Conditional Probability and that the formula for conditional probability is =
= Probability(A/F) = 0.03/0.2
=Probability for the given problem = 3/20 (iii)
Hence, the probability that a student is absent given that today is Friday is 3/20.
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I need help with this problem doing the Pythagorean theorem
x=square root 57
(somewhere to 7.5)
a new extended-life lightbulb has an average life of 750 hours, with a standard deviation of 50 hours. if the life of these lightbulbs approximates a normal distribution, about what percent of the distribution will be between 600 hours and 900 hours?
The typical lifespan of a brand-new extended-life light bulb is 750 hours, with a standard deviation of 50 hours. If these light bulbs' lifespans roughly follow a normal distribution , then 99.7% of the distribution will fall between 600 and 900 hours.
According to the Empirical Rule , 68% of measurements for a randomly distributed variable with a normal distribution are within one standard deviation of the mean.Within two standard deviations of the mean, 95% of the measurements are.
99% of the measurements fall within a 3 SD range of the mean.
This issue involves that:
50 is the standard deviation
Approximately proportion of the distribution will fall in the range of 600 to 900 hours,
600 = 750 - 3*50
Three standard deviations away from the mean is 600.
900 = 750 + 3*50
3 standard deviations are added to the mean, or 900.
According to the Empirical Rule, between 600 and 900 hours will make up 99.7% of the distribution.
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can you please answer this? its timed so dont take too long!
The equivalent of the expression [tex]\frac{(-7m^{4}+15m^{3}-12m^{2} )+(3m^{5}-12m^{4}-7m^{3} )}{m-6}[/tex] is 3m⁴ - 19m³ + 8m² - 12m
Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
Equivalent algebraic expressions are those expressions which on simplification give the same resulting expression . Therefore, let's simplify the expression to get the equivalent.
[tex]\frac{(-7m^{4}+15m^{3}-12m^{2} )+(3m^{5}-12m^{4}-7m^{3} )}{m-6}[/tex]
[tex]\frac{3m^{5} -7m^{4}-12m^{4}+15m^{3}-7m^{3}-12m^{2} }{m-6}[/tex]
[tex]\frac{3m^{5} -19m^{4}+8m^{3}-12m^{2} }{m-6}[/tex]
3m⁴ - 19m³ + 8m² - 12m
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Sydney measured a line to be 4.9 inches long. If the actual length of the line is 5.2 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
The percent error of the measurement of lengths is 5.8%.
Given that, Sydney measured a line to be 4.9 inches long.
Percentage is defined as a given part or amount in every hundred . It is a fraction with 100 as the denominator and is represented by the symbol "%".
The actual length of the line is 5.2 inches
Difference of measure = 5.2-4.9 =0.3
The percent error = 0.3/5.2 ×100
= 0.0576×100
Therefore, the percent error of the measurement of lengths is 5.8%.
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Suppose a researcher decided to test a hypothesis that adding compost to tomato plants increases mean tomato mass. She knew the standard deviation of the mass of all tomato plants, so she chose a one-sample z‑test using a simple random sample of 50 plants that received compost. She used a significance level of α=0.05. The power of her test to detect a difference in mean tomato mass of 25 g or more was 0.98. What is the probability, β, that the researcher will make a type II error and fail to conclude that adding compost increases mean tomato mass when, in fact, adding compost increases mean tomato mass by 25 g or more? Give your answer as a decimal, precise to two decimal places. β=
The value of β from the power of test is obtained as 0.02
The chance of rejecting the null hypothesis as untrue, or the likelihood of avoiding a type II mistake, is the power of a test . The probability that a certain investigation will identify a departure from the null hypothesis if one exists is another way to conceptualize power.
In hypothesis testing , power is typically the main concern. Power is defined as the likelihood that we would reject H0 as untrue, i.e., power = 1-β . Power is the likelihood that a test would properly reject a null hypothesis that isn't true.
The specified value for the test's power is 0.98 in the problem.
Type II error, β= 1 - Power = 1 - 0.98 = 0.02
So, the value of β is obtained as 0.02.
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will give brainiest need help asap!! what is the equation of the following graph in vertex form? y = (x − 2)2 + 1 y = (x − 1)2 + 2 y = (x + 2)2 + 1 y = (x + 2)2 − 1
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Given graph has vertex at (2, 1) .
The matching choice is A
highway bridges in the united states were categorized as structurally deficient, functionally obsolete, or safe. about 26% of the bridges were found to be structurally deficient, while 19% were functionally obsolete. a. what was the population or sample of interests?
The population of interest was The condition of highway bridges in the united states
According to the question,
Highway bridges in the united states were categorized as structurally deficient, functionally obsolete, or safe.
Percentage of bridges found to be structurally deficient = 26%
Percentage of bridges found to be functionally obsolete = 19%
The condition of highway bridges in the united states is the population researchers are interested
The main reason researchers are interested in the condition because the highway bridges can be classified as being structurally deficient or could be safe, or could be obsolete functionally.
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The population of bats in a large cave is 8500 and is growing exponentially at 10% per year. Write a function to represent the population of bats after t t years, where the quarterly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per quarter, to the nearest hundredth of a percent.
The yearly exponential model for the population of bats is C'(t) = 8500 · 1.1ⁿ and the quarterly percentage rate is 2.41 %.
In this question we must determine the exponential model that represents the population of bats , whose model is shown below:
C'(t) = C · (1 + r / 100)ⁿ
The yearly exponential model is represented by: (C = 8500, r = 10)
C'(t) = 8500 · 1.1ⁿ
The quarterly rate of change can be found by using the following expression:
(1 + 10 / 100) = (1 + r' / 100)⁴
1.1 = (1 + r' / 100)⁴
1 + r' / 100 = 1.024
r' / 100 = 0.02411
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If a connected planar graph has 10 regions and 21 edges, how many vertices does it have?
thirty three vertical edges
karlie and her friend can paint 6/7 of an picture in 3/14 of an hour. How much paintings can they paint in a hour
The paintings that Karlie and her friend can paint in a hour is 4.
It's important to note that this question has to do with the division of fractions . In this case, Karlie and her friend can paint 6/7 of an picture in 3/14 of an hour.
The painting that can be done in 1 hour will be the division of the fractions given. This will be:
= 6/7 ÷ 3/14
= 6/7 × 14/3
The number of paintings is 4.
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If the mean of a negatively skewed distribution is 64, which of these values could be the median of the distribution? OA. 64 B. 56 C. 68 O D. 60 APEX
The median value must be higher than the mean , which is 68 in this case, so option C is correct .
Mean is a measurement of a probability distribution's central tendency along the median and mode . It also goes by the name "anticipated value."
The mean of a negatively skewed distribution is 64.
Calculate the median by hit and trial method,
When a distribution is negatively skewed, the distribution curve will not fall equally on either side of the median. The distribution curve will be shifted even more toward the bottom end. It will be so far below if the median value is only marginally below the median.
Therefore, the median value must be higher than the mean, which is 68 in this case.
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A length is measured as 21 cm correct to 2 significant figures. a) What is the lower bound for the length? b) What is the upper bound for the length?
Devin found the equation of the parabola that fits the three points in the table to be y = 0. 345x ^ 2 - 0. 57x - 2. 78. Devin correct? Explain
Devin found the wrong equation of the parabola that fits the three points .
A parabola is a curve which forms by joining all the points which are at an equal distance from a fixed point (the focus) and a fixed straight line (the directrix).
Given is Devin found the equation of the parabola that fits the three points in the table to be y = 0.345x² - 0.57x - 2 .
We have the following table -
[x] [y]
4 5
0.6 3
9 20
We have the equation of the parabola as -
y = 0.345x² - 0.57x - 2 .
Plot the graph of the parabola . It can be seen that the points don't lie on the parabola. So, he is incorrect.
Therefore, Devin found the wrong equation of the parabola that fits the three points .
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What is the name of the element The charge The mass number The atomic number
Answer:Beryllium
Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (Enter your answers as a comma-separated list.) 7xe, a = 0 Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (Enter your answers as a comma-separated list.) f(x) = 2 cos(x), a = 0 Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that R, (x) 0.] cos(3x) f(x) 8 f(x) = M8 n = 0 Find the associated radius of convergence R. R= Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that R, (x) +0.] f(x) = 4 cos(x), a = 57 f(x) = n = 0 Find the associated radius of convergence R. R = Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) 6x2 + 1 f(x) = Î n = 0 Determine the interval of convergence. (Enter your answer using interval notation.)
So the Taylor series for the function informed will be:
7x, 7x², 21/6 x³, 7/6 x⁴
The function is:
f(x) = 7eˣx
WE need to use the definition of a Taylor series to find the first four non zero terms of the series for f(x) centered at the given value of a.
f(x) = ∑ (fⁿ(a) (x - a)ⁿ)/n!
The first four terms will be:
f(x) = f(0) + f(1) + f(2) + f(3)
f(x) = (f(a) (0- a)ⁿ)/n! + (f'(a) (1 - a)ⁿ)/1! + (f''(a) (2 - a)²)/2! + (f'''(a) (3 - a)³)/3!
Therefore, the four first terms are 7x, 7x², 21/6 x³, 7/6 x⁴
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What is the slope of the line that passes through the points (-4, -10) and (-7, -19)? Write your answer in the simplest form.
Below, I have attached the slope formula. Inserting the numbers into the formula, we get 9/3=3
3x to the second power-2x-5
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A hypothesis is an assumption or idea that is proposed for the sake of argument or testing. Learn the difference between hypothesis and theory, synonyms, examples, and word history of hypothesis.
HYPOTHESIS definition: 1. an idea or explanation for something that is based on known facts but has not yet been proved…. Learn more.
Hypothesis definition: a proposition, or set of propositions, set forth as an explanation for the occurrence of some specified group of phenomena, either asserted merely as a provisional conjecture to guide investigation (working hypothesis ) or accepted as highly probable in the light of established facts.. See examples of HYPOTHESIS used in a sentence.
A hypothesis is an idea or explanation for something that is based on known facts but has not yet been proved. Learn more about the meaning, usage and pronunciation of hypothesis with examples from various sources.
A hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation.
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A different meaning of the term hypothesis is used in formal logic, to denote the antecedent of a proposition; thus in the proposition "If P, then Q ", P denotes the hypothesis (or antecedent); Q can be called a consequent. P is the assumption in a (possibly counterfactual) What If question. The adjective hypothetical, meaning "having the nature of a hypothesis", or "being assumed to exist as ...
hypothesis: 1 n a tentative insight into the natural world; a concept that is not yet verified but that if true would explain certain facts or phenomena "a scientific hypothesis that survives experimental testing becomes a scientific theory" Synonyms: possibility , theory Types: show 17 types... hide 17 types... hypothetical a hypothetical ...
hypothesis, something supposed or taken for granted, with the object of following out its consequences (Greek hypothesis, "a putting under," the Latin equivalent being suppositio ). Discussion with Kara Rogers of how the scientific model is used to test a hypothesis or represent a theory. Kara Rogers, senior biomedical sciences editor of ...
Definition of hypothesis noun in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
A hypothesis is a proposed explanation for an observation, often tested by an experiment. Learn the difference between null and alternative hypotheses, how to write a hypothesis and see examples of hypotheses in science and logic.
A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection.
3 meanings: 1. a suggested explanation for a group of facts or phenomena, either accepted as a basis for further verification.... Click for more definitions.
Scientific hypothesis is an idea that tries to explain a natural phenomenon based on observation or experimentation. Learn how to formulate and test a scientific hypothesis, and what makes it different from other types of hypotheses, with examples from various fields of science.
Hypothesis is an idea or prediction that scientists make before they do experiments. Click to learn about its types, and importance of hypotheses in research and science. Take the quiz!
A hypothesis is a prediction of what will be found at the outcome of a research project and is typically focused on the relationship between two different variables studied in the research. It is usually based on both theoretical expectations about how things work and already existing scientific evidence. Within social science, a hypothesis can ...
Learn exactly what a research hypothesis (or scientific hypothesis) is with Grad Coach's clear, plain-language definition, including loads of examples.
A research hypothesis, in its plural form "hypotheses," is a specific, testable prediction about the anticipated results of a study, established at its outset. The research hypothesis is often referred to as the alternative hypothesis.
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Hypothesis Testing for One Mean Examples Learning Objectives. In this section, we will perform left, right and two-tailed hypothesis tests for means from one sample. In this section, we will step through several examples of how to perform hypothesis testing for sample means.
A null hypothesis is that the mean nose lengths of men and women are the same. The alternative hypothesis is that women have a shorter mean nose length than men. Alpha for the problem is.05. A statistical test is done and the p-value is 0.04. Which of the following is the most appropriate way to state the conclusion?