Question 10 • 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. What are the appropriate hypotheses?
Answer
A
H0: μ = 76.4 versus Ha: μ < 76.4, where μ = the true mean height of all trucks
B
H0: μ = 76.4 versus Ha: μ > 76.4, where μ = the true mean height of all trucks
C
H0: μ = 76.4 versus Ha: μ < 77.1, where μ = the true mean height of all trucks
D
H0: μ = 76.4 versus Ha: μ > 77.1, where μ = the true mean height of all trucks
Explanation
The question asks whether the true mean height of all trucks is greater than 76.4 inches, so the alternative hypothesis is μ > 76.4. The null hypothesis uses equality at the stated benchmark: μ = 76.4. The sample mean of 77.1 inches is evidence used in the test, not the value that defines the hypotheses. Therefore, the correct choice is B.
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