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 point 4 minutes with a standard deviation of 5 point 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 ratio of cap h sub 0 to mu is equal to 20 versus ratio of cap h sub A to mu is greater than 20 , where mu is equal to the true mean travel time for all students who attend this school. The conditions for inference are met. What are the appropriate test statistic and cap p -value? Use the t -table.
Answer
A
t is equal to negative 2 point 8 8 ; the cap p -value is between 0 point 0 0 2 5 and 0 point 0 0 5 .
B
t is equal to 2 point 8 8 ; the cap p -value is between 0 point 0 0 2 5 and 0 point 0 0 5 .
C
t is equal to 2 point 8 8 ; the cap p -value is 0 point 0 0 2 0 .
D
t is equal to negative 2 point 8 8 ; the cap p -value is 0 point 0 0 2 0 .
Explanation
Use the one-sample t statistic: (22.4 − 20) ÷ (5.9 ÷ √50) ≈ 2.88. With 49 degrees of freedom and a greater-than alternative, this positive statistic gives a one-sided P-value between 0.0025 and 0.005 in the t-table. Thus the correct choice is t = 2.88 with a P-value in that interval.
AI-written and checked against the verified answer.