Question 7 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
An engineer would like to design a parking garage in the most cost-effective manner. He reads that the average height of pickup trucks, which is the largest type of vehicle that should be expected to fit into the parking garage is 76.4 inches. To double-check this figure, the engineer employs a statistician. The statistician selects a random sample of 100 trucks and finds the mean height of the sample to be 77.1 inches with a standard deviation of 5.2 inches. The statistician will determine if these data provide convincing evidence that the true mean height of all trucks is greater than 76.4 inches. The statistician plans to test the hypotheses, H0: μ = 76.4 versus Ha: μ > 76.4, where μ = the true mean height of all trucks. The conditions for inference are met. What are the appropriate test statistic and P-value?Find the t-table here and the z-table here.
Answer
A
t = 1.35. The P-value is 0.9145.
B
z = 1.35. The P-value is 0.0885.
C
t = 1.35. The P-value is between 0.05 and 0.10.
D
z = 1.35. The P-value is between 0.05 and 0.10.
Explanation
Because the population standard deviation is unknown and the sample standard deviation is used, use a t statistic. Calculate t = (77.1 − 76.4)/(5.2/√100) = 0.7/0.52 ≈ 1.35, with 99 degrees of freedom. For the upper-tail alternative, this gives a P-value between 0.05 and 0.10, so the correct choice is C: t = 1.35 and the P-value is between 0.05 and 0.10.
AI-written and checked against the verified answer.