greater than (>) less than (<)
H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.
H 0 : No more than 30% of the registered voters in Santa Clara County voted in the primary election. p = 30
H a : More than 30% of the registered voters in Santa Clara County voted in the primary election. p > 30
A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.
H 0 : The drug reduces cholesterol by 25%. p = 0.25
H a : The drug does not reduce cholesterol by 25%. p ≠ 0.25
We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:
H 0 : μ = 2.0
H a : μ ≠ 2.0
We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, <, >) for the null and alternative hypotheses. H 0 : μ __ 66 H a : μ __ 66
We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:
H 0 : μ = 5
H a : μ < 5
We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, <, >) for the null and alternative hypotheses. H 0 : μ __ 45 H a : μ __ 45
In an issue of U.S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.
H 0 : p = 0.066
H a : p > 0.066
On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol (=, ≠, <, >) for the null and alternative hypotheses. H 0 : p __ 0.40 H a : p __ 0.40
In a hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis , typically denoted with H 0 . The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality (=) Always write the alternative hypothesis , typically denoted with H a or H 1 , using less than, greater than, or not equals symbols, i.e., (≠, >, or <). If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis. Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.
H 0 and H a are contradictory.
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For example, some textbooks will say:
$$H_o:\mu≤0$$ $$H_a:\mu>0$$
If the null hypothesis claims that there's no effect/change, how could the null hypothesis be anything other than $H_o=μ$?
I think the issue is over acceptance of a rule of thumb. That's the problem with thumbs making rules.
My guess is that you've heard something like "the null hypothesis is that there's no effect". But it would be much more accurate to say something along the lines of "often, the null hypothesis is that there's no effect". If $\mu$ is the effect of interest, then certainly $H_o: \mu = 0$ can be correctly interpreted as the null hypothesis being that there's no effect (to be pedantic and circular, this is assuming $\mu=0$ implies no effect. This would not be the case if $\mu$ was a multiplicative factor, for example).
But hypothesis testing is much more general than that special case. You are really testing one set of potential parameters, whether it be $\mu = 0$ or $\mu \leq 0$ against another set of parameters. In theory, there's nothing that limits the structure of the two sets of hypothesis that you choice to construct.
That's theory. Let's talk practice. Recall the fact that we never accept the null hypothesis, but rather at best fail to reject it. On the other hand, through hypothesis testing, we can observe enough evidence to conclude that the parameter belongs to the alternative hypothesis set. Because of this, it makes sense to set up your hypotheses such that from a scientific standpoint, it is very interesting to know that the parameter is in the alternative hypothesis set. So when you design your hypothesis test, your alternative hypothesis should be what your interested in showing, i.e. your drug has a positive effect. As such, your null hypothesis should be the "uninteresting" results, i.e. your drug does not have a positive result.
The null hypothesis can be anything at all. It has nothing to do with "nullness" of effect. Usual tests are built to have an arbitrarily low type I error (ie. $\alpha$), so that we don't mistake the null hypothesis being false when in fact it is true.
For example, in a correlations test we set $H_0: \rho = 0$, so that:
In conclusion: the null hypothesis should be the one you care about the most not rejecting when it is true.
You talk about one and two tailed tests ,the one-tailed tests allow for the possibility of an effect in just one direction , where with two-tailed test you are testing for the possibility of an effect in two directions , so when you reject the null hypothesis in one tailed test you reject that there is no effect and you reject that there is an effect in the direction which you do not care about it.So in your case $$H_o:\mu≤0$$ when you reject $H0$ you reject both "There is no effect " and "There is a negative effect ". Here there is a nice discussion about One-Tailed vs Two-Tailed Tests? and how a two-tailed test splits your significance level .
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The null statement must always contain some form of equality (=, ≤ or ≥) Always write the alternative hypothesis, typically denoted with H a or H 1, using less than, greater than, or not equals symbols, i.e., (≠, >, or <). If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis.
Revised on June 22, 2023. The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test: Null hypothesis (H0): There's no effect in the population. Alternative hypothesis (Ha or H1): There's an effect in the population. The effect is usually the effect of the ...
The null states that the infection rates for the control and treatment groups are equal. Null Hypothesis H 0: Group proportions are equal in the population: p 1 = p 2. Alternative Hypothesis H A: Group proportions are not equal in the population: p 1 ≠ p 2. Correlation and Regression Coefficients.
If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis, typically denoted with \(H_{0}\). The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality \((=, \leq \text{or ...
The null and alternative hypotheses are both statements about the population that you are studying. The null hypothesis is often stated as the assumption that there is no change, no difference between two groups, or no relationship between two variables. The alternative hypothesis, on the other hand, is the statement that there is a change ...
In scientific research, the null hypothesis (often denoted H 0) ... Null hypotheses that assert the equality of effect of two or more alternative treatments, for example, a drug and a placebo, are used to reduce scientific claims based on statistical noise. This is the most popular null hypothesis; It is so popular that many statements about ...
The actual test begins by considering two hypotheses.They are called the null hypothesis and the alternative hypothesis.These hypotheses contain opposing viewpoints. H 0, the —null hypothesis: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.
The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test: Null hypothesis (H0): There's no effect in the population. Alternative hypothesis (HA): There's an effect in the population. The effect is usually the effect of the independent variable on the dependent ...
If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis, typically denoted with \(H_{0}\). The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality \((=, \leq \text{or ...
H 0 (Null Hypothesis): Population parameter =, ≤, ≥ some value. H A (Alternative Hypothesis): Population parameter <, >, ≠ some value. Note that the null hypothesis always contains the equal sign. We interpret the hypotheses as follows: Null hypothesis: The sample data provides no evidence to support some claim being made by an individual.
The actual test begins by considering two hypotheses. They are called the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints. H0 H 0: The null hypothesis: It is a statement of no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.
1. In traditional hypothesis testing the null hypothesis always contains an -sign, whether it is as or. The mull hypothesis determines the null distribution of the test statistic. Hence also the critical value used in testing at a particular level or, in computer programs, the P-value. Example: In a simple binomial test whether a coin is fair ...
rue. The null hypothesis (denoted by H0) is a hypothesis that contains a statement of equality, =.The alternative hypo. If the claim value is k and the population parameter is p, then some possible pairs of null and alternative hypothesis are. H0: p = k. = kH0: p = kH1: p > kH1: p < kH1: pIde.
When your p-value is less than or equal to your significance level, you reject the null hypothesis. In other words, smaller p-values are taken as stronger evidence against the null hypothesis. Conversely, when the p-value is greater than your significance level, you fail to reject the null hypothesis. In this case, the sample data provides ...
The null hypothesis always involves some kind of equality (=, ... As expected under the null hypothesis, this distribution is centered at zero (the mean of the distribution is -0.016. From the figure we can also see that the distribution of t values after shuffling roughly follows the theoretical t distribution under the null hypothesis (with ...
If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis, typically denoted with \(H_{0}\). The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality \((=, \leq \text{or ...
Definitions Null Hypothesis ( H 0) Statement of zero or no change. If the original claim includes equality (<=, =, or >=), it is the null hypothesis.If the original claim does not include equality (<, not equal, >) then the null hypothesis is the complement of the original claim. The null hypothesis always includes the equal sign. The decision is based on the null hypothesis.
The actual test begins by considering two hypotheses.They are called the null hypothesis and the alternative hypothesis.These hypotheses contain opposing viewpoints. H 0: The null hypothesis: It is a statement of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.
The Equality Null Hypothesis, also known as the Simple Null Hypothesis, is a fundamental concept in statistical hypothesis testing that assumes no difference, effect or relationship between groups, conditions or populations being compared. Non-Inferiority Null Hypothesis.
The null statement must always contain some form of equality (=) Always write the alternative hypothesis, typically denoted with H a or H 1, using less than, greater than, or not equals symbols, i.e., (≠, >, or <). If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis.
You are testing two hypotheses which, to avoid having to write them out in full each time, we denote by H0 H 0 (null) and H1 H 1 (alternative). When we write, say, H0: μ ≤ 0 H 0: μ ≤ 0, we are merely defining the null hypothesis (here, that μ ≤ 0 μ ≤ 0 ). When we write H1: μ > 0 H 1: μ > 0, we are defining the alternative.