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The parking office now decides that it is too risky to make claims aboutpopulation proportions. Instead, they now only claim that the attitudes regardingthe new parking policy are independent of student, faculty or administration status.Test this claim at a significance level of α = 5%, clearly stating your hypotheses.Past Final Examination 1 Page 4 of 7 STAT7055

Question

The parking office now decides that it is too risky to make claims aboutpopulation proportions. Instead, they now only claim that the attitudes regardingthe new parking policy are independent of student, faculty or administration status.Test this claim at a significance level of α = 5%, clearly stating your hypotheses.Past Final Examination 1 Page 4 of 7 STAT7055

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Solution

To test the claim that attitudes regarding the new parking policy are independent of student, faculty, or administration status, we would use a chi-square test for independence. Here are the steps:

  1. State the Hypotheses: The null hypothesis (H0) is that the attitudes regarding the new parking policy are independent of student, faculty, or administration status. The alternative hypothesis (H1) is that the attitudes regarding the new parking policy are not independent of student, faculty, or administration status.

  2. Choose an Alpha Level: In this case, the problem has provided an alpha level of 0.05 (5%).

  3. Calculate the Expected Frequencies: This involves creating a contingency table of observed frequencies, then calculating the expected frequencies based on the assumption that H0 is true.

  4. Calculate the Test Statistic: The test statistic is a chi-square statistic, which is calculated using the observed and expected frequencies.

  5. Determine the P-Value: The P-value is the probability of observing a chi-square statistic as extreme as, or more extreme than, the observed statistic under the null hypothesis. This can be found using a chi-square distribution table or a statistical software.

  6. Compare P-Value and Alpha Level: If the P-value is less than or equal to the alpha level, reject the null hypothesis. If the P-value is greater than the alpha level, do not reject the null hypothesis.

  7. Make a Decision: Based on the comparison from step 6, make a decision about whether to reject or not reject the null hypothesis. If we reject the null hypothesis, we conclude that the attitudes regarding the new parking policy are not independent of student, faculty, or administration status. If we do not reject the null hypothesis, we do not have enough evidence to conclude that the attitudes are not independent.

Remember, failing to reject the null hypothesis does not prove it is true. It simply means that there is not enough evidence against it.

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