Katie Sr Yr Stats final practice set 6 (problem 13)

Problem 17: Comparing Online Shopping Rates A researcher wants to test whether a higher proportion of urban residents shop online compared to rural residents. In a survey, 280 out of 320 urban residents and 250 out of 310 rural residents reported shopping online in the past month. Use a 0.05 significance level to test the claim. Hypotheses What are the null and alternative hypotheses?

• H0:p1=p2,H1:p1≠p2

• H0:p1=p2,H1:p1>p2

• H0:p1>p2,H1:p1=p2

• H0:μ1=μ2,H1:μ1≠μ2

Problem 2: Type of Test - What type of test is appropriate?

• 1-sample z-test

• 2-proportion z-test

• 1-sample t-test

• Chi-square test for independence

Problem 3: Test Statistic - What is the test statistic?

• 2.10

• 1.34

• 0.87

• 2.35

Problem 4: P-value - What is the P-value?

• 0.0179

• 0.0712

• 0.0380

• 0.0093

Problem 5: Decision - What is the appropriate decision at α = 0.05?

• Fail to reject H0

• Reject H0

• Use a two-tailed test instead

• Retest with a larger sample

Problem 6: Conclusion - What is the correct conclusion?

• There is strong evidence that urban residents shop online less than rural residents.

• There is strong evidence that urban residents shop online more than rural residents.

• There is no evidence of a difference in online shopping rates.

• The sample size was too small to conclude anything.

Problem 7: Comparing Gym Membership Rates A health researcher wants to test whether a higher proportion of people in City A have gym memberships compared to people in City B. In a survey, 195 out of 240 people in City A and 165 out of 230 people in City B reported having active gym memberships. Use a 0.05 significance level to test the claim. Hypotheses - What are the null and alternative hypotheses?

• H0:p1=p2,H1:p1>p2

• H0:p1=p2,H1:p1=p2

• H0:p1>p2,H1:p1=p2

• H0:μ1=μ2,H1:μ1>μ2

Problem 8: Type of Test - What type of test is appropriate?

• 1-sample z-test

• 2-proportion z-test

• 1-sample t-test

• Chi-square test for independence

Problem 9: Test Statistic - What is the test statistic?

• 1.68

• 2.44

• 3.12

• 1.21

Problem 10: P-value - What is the P-value?

• 0.0073

• 0.042

• 0.018

• 0.112