17
RCMultiple Choice

Unit Test — Cumulative exam

Question 17 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)

The amount of time it takes students to travel to school can vary greatly depending on how far a student lives from the school and what mode of transportation they take to school. A student claims that the average travel time to school for his large district is 20 minutes. To further investigate this claim, he selects a random sample of 50 students from the school and finds that their mean travel time is 22.4 minutes with a standard deviation of 5.9 minutes. He would like to conduct a significance test to determine if there is convincing evidence that the true mean travel time for all students who attend this school is greater than 20 minutes. The student would like to test H0: μ = 20 versus Ha: μ > 20, where μ = the true mean travel time for all students who attend this school. The conditions for inference are met. The test statistic is t = 2.88 and the P-value is between 0.0025 and 0.005. What conclusion should be made at the significance level, ?

Question illustration
Answer
A
Reject H0. There is convincing evidence that these students traveled more than 20 minutes to attend this school.
B
Reject H0. There is convincing evidence that the true mean travel time for all students who attend this school is greater than 20 minutes.
C
Fail to reject H0. There is not convincing evidence that these students traveled more than 20 minutes to attend this school.
D
Fail to reject H0. There is not convincing evidence that the true mean travel time for all students who attend this school is greater than 20 minutes.
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