A city planner is comparing traffic patterns at two different intersections. He randomly selects two times between 6 am and 10 pm, and he and his assistant count the number of cars passing through each intersection during the 10-minute interval that begins at that time. He plans to test the hypothesis that the mean difference in the number of cars passing through the two intersections during each of those two time intervals is 0. Which of the following is an appropriate test of the city planner's hypothesis? (a) Two-proportion z-test (b) Two-sample z-test for a difference in means (c) Two proportion t-test (d) Paired t-test for a mean difference (e) Two-sample t-test for a difference in means
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A city planner is comparing traffic patterns at two different intersections. He randomly selects 12 times between 6 am and 10 pm and he and his assistant count the number of cars passing through each intersection during the 10-minute interval that begins at that time. He plans to test the hypothesis that the mean difference in the number of cars passing through the two intersections during each of those 12 time intervals is zero. Which of the following is an appropriate test of the city planner's hypothesis? (A) Two-sample t-test (B) Two-sample z-test (C) Matched pairs t-test (D) Two-proportion t-test (E) Two-proportion z-test
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A driving instructor is investigating whether the time a driver spends in a driver's education course improves their score on the driver's test. The instructor randomly selected 10 drivers from a driver's education course and recorded the number of hours each driver attended the driver's education course and their corresponding score on the driver's test. Assuming all conditions for inference are met, which of the following significance tests should be used for the investigation? A chi-square test of independence A two-sample t-test for a difference between means A two-sample z-test for a difference between proportions A linear regression t-test for slope A matched pairs t-test for a mean difference
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Mark Bates, a statistics professor at Oxnard College, recorded his commuting times using three different routes from home to work. The routes are named for the streets on which he traveled, and the times are in seconds. a. For the boxplots given, compare the medians, interquartile ranges, and shapes, and mention any potential outliers. b. Assuming that the overall significance level is $0.05$, what is the Bonferroni-corrected level of significance for each pair of comparisons? c. Carry out $t$ -tests to compare the means of all pairs, and summarize your findings by reporting $t$ -statistics, p-values, and conclusions. Assume that the conditions for using two-sample $t$ -tests are met.
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