Hypothesis Test: Chi-Square Test of Variance
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Hypothesis Test:
Null: "Older people are more likely to buy American cars than younger people."
Alternative: "Older people are not more likely to buy American cars than younger people."
(please refer to the attachment for data)
1. State the null and alternate hypothesis.
2. Select the level of significance - the alpha value.
3. Choose the test statistic to use.
4. Determine the decision rule - the critical value of the test statistic.
5. Use the sample data to compute the test statistic based on the sample, and determine whether to reject the null or not.
The null hypothesis that is being discussed is whether older people are more likely to buy American cars than younger people. The alternative hypothesis is that older people are not more likely to buy American cars than younger people. When discussing null hypothesis, look at Type I and Type II errors. Type I errors are also called the level of significance.
A Type I error is that we will wrongly reject a true H0. An example of a Type I error would be if it was chosen to use a decision rule using alpha = .05, we would expect to commit a Type I error about 5 times in 100. Type II errors is when the probability that the test statistic falls in the acceptance region even thought the null hypothesis is false.
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Solution Summary
The solution provides step-by-step method of performing a hypothesis test. All the steps of hypothesis testing (formulation of null and alternate hypotheses, selection of significance level, choosing the appropriate test-statistic, decision rule, calculation of test-statistic and conclusion) have been explained in details. The solution also provides information on when to use a parametric test and when to use a non-parametric test.
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Formulation of Null Hypothesis:
The Null Hypothesis is always stated as the assertion that the things we are testing ARE NOT ...
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- MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)
- BSc, Banaras Hindu University
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