8
QuizMultiple Choice

Testing a Claim about a Difference between Means

Question 8 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)

Timmy could follow two main routes to get to school. Timmy believes that route 1 is faster than route 2. To investigate, he decides to keep track for the next 4 weeks. Each morning, he flips a coin to determine which route he takes. Of the 20 school days, 12 days were randomly assigned to route 1, and 8 days were randomly assigned to route 2. The mean travel time for days assigned to route 1 was 20 minutes with a standard deviation of 3 minutes. The mean travel time for the days assigned to route 2 was 22 minutes with a standard deviation of 2 minutes. Timmy would like to know if the data provide convincing evidence of a difference in travel time for the 2 routes, so he tests H0: μ1 – μ2 = 0, Ha: μ1 – μ2 ≠ 0. Let μ1 = the true mean travel time to school along route 1 and μ2 = the true mean travel time to school along route 2. Dotplots of the distribution of travel time for route 1 and route 2 show no strong skewness or outliers. The conditions for inference have been met. The standardized test statistic is t = –1.79, and the P-value is between 0.05 and 0.10. What conclusion should be made using the significance level, = 0.05?

Question illustration
Answer
A
Reject H0. There is convincing evidence that the true mean travel time for route 1 differs from the true mean travel time for route 2.
B
Reject H0. There is convincing evidence that the sample mean travel time for route 1 differs from the sample mean travel time for route 2.
C
Fail to reject H0. There is not convincing evidence that the true mean travel time for route 1 differs from the true mean travel time for route 2.
D
Fail to reject H0. There is not convincing evidence that the sample mean travel time for route 1 differs from the sample mean travel time for route 2.
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