## Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

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### Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

The test statistic for the χ^{2} test of independence involves comparing observed (sample data) and expected frequencies in each cell of the table. The expected frequencies are computed assuming that the null hypothesis is true. The null hypothesis states that the two variables (the grouping variable and the outcome) are independent. The definition of independence is as follows:

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### Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

407) suggested that “an investigator would be misled less frequently and would be more likely to obtain the information he seeks were he to formulate his experimental problems in terms of the estimation of population parameters, with the establishment of confidence intervals about the estimated values, rather than in terms of a null hypothesis against all possible alternatives.”Many other critics have echoed that advice, to which we also subscribe, especially when the outcome measure is well defined.

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If the null hypothesis were true (i.e., no change from the prior year) we would have expected more students to fall in the "No Regular Exercise" category and fewer in the "Regular Exercise" categories. In the sample, 255/470 = 54% reported no regular exercise and 90/470=19% reported regular exercise. Thus, there is a shift toward more regular exercise following the implementation of the health promotion campaign. There is evidence of a statistical difference, is this a meaningful difference? Is there room for improvement?

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## (1997).In praise of the null hypothesis statistical test.

The p-value tells you how unlikely this sample (ora more extreme one) is if the null hypothesis is true. The moreunlikely (surprising, unexpected), the lower the p-value, and the more confident you can feelabout rejecting H_{0}.

## Null and Alternative Hypothesis | Real Statistics Using …

We now compute the expected frequencies using the sample size and the proportions specified in the null hypothesis. We then substitute the sample data (observed frequencies) into the formula for the test statistic identified in Step 2. We organize the computations in the following table.

## How to Determine a p-Value When Testing a Null Hypothesis

The null hypothesis in the χ^{2} test of independence is often stated in words as: ** H_{0}: The distribution of the outcome is independent of the groups. The alternative or research hypothesis is that there is a difference in the distribution of responses to the outcome variable among the comparison groups** (i.e., that the distribution of responses "depends" on the group). In order to test the hypothesis, we measure the discrete outcome variable in each participant in each comparison group. The data of interest are the observed frequencies (or number of participants in each response category in each group). The formula for the test statistic for the χ

^{2}test of independence is given below.

## Null hypothesis: μ = 72 Alternative ..

We now compute the expected frequencies using the sample size and the proportions specified in the null hypothesis. We then substitute the sample data (observed frequencies) into the formula for the test statistic identified in Step 2. We organize the computations in the following table.

## Hypothesis Testing The null and alternative ..

In a nice phrase,say that p-values “measure the strength of the evidence againstthe null hypothesis; the smaller the p-value, the stronger theevidence against the null hypothesis.” They also quote oninterpreting a p-value:“If P is between 0.1 and 0.9 there is certainly no reason tosuspect the hypothesis tested. If it is below 0.02 it is stronglyindicated that the hypothesis fails to account for the whole of thefacts. We shall not often be astray if we draw a conventional line at0.05.”