Use the following information to answer the remaining questions: Janice and her cousin Linda are a little competitive about the relative merits of their home towns, Vancouver and Victoria, respectively. One contest they had was to determine if the proportion of rainy days was significantly different for their home towns. They found weather records on the internet and each of them randomly selected 60 days from the past 5 years. Janice found that there had been measurable rainfall on 17 of the 60 days she selected for Vancouver and Linda found that there had been measurable rainfall on 12 of the 60 days she selected for Victoria. They intend to perform a test of significance on their data, using the hypotheses H0: p_Van – p_Vic = 0 versus HA: p_Van – p_Vic ≠ 0 and the 0.05 significance level.
a)When calculating the test statistic, what is the standard deviation of the sampling distribution of the difference in proportions? Hint: As we observed back in Ch 4, the standard error is the standard deviation of the sampling distribution
2.686
0.078
7.477
0.110
b) Suppose that Janice and Linda’s test statistic is 1.07. Which of the following is closest to the appropriate P-value for the test? Then make your decision for this test: Would you reject H0 or fail to reject H0 at a 0.05 significance level?
0.1423; Reject H0
0.0446; Reject H0
0.1449; Fail to reject H0
0.1423; Fail to reject H0
0.2846; Fail to reject H0
0.2846; Reject H0
Bonus (worth 1 mark): Which of the following best describes what it would mean if Janice and Linda’s test resulted in a Type I error?
-Accepting the alternative hypothesis instead of rejecting the null hypothesis.
-Concluding that there is no difference in the proportion of rainy days in the two cities when there is a difference.
-Accepting the null hypothesis instead of rejecting the alternative hypothesis.
-Choosing the wrong test procedure, such as using a z-test instead of a t-test.
-Concluding that there is a difference in the proportion of rainy days in the two cities when there is no difference.
