Question

1. It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 36 small cars at 65 miles per hour and records the braking distance. The sample average braking distance is computed as 114 feet. Assume that the population standard deviation is 22 feet.

a. Set up the null and the alternative hypotheses for the test.

b. Calculate the value of the test statistic.

c. Find the p-value.

d. Calculate the critical value using α = 0.01

e. Use α = 0.01 to determine if the average breaking distance differs from 120 feet.

2. Consider the following hypotheses:
H₀: μ ≤ 12.6
H_A: μ > 12.6
A sample of 25 observations yields a sample mean of 13.4. Assume that the sample is drawn from a normal population with a population standard deviation of 3.2.

a. Calculate the value of the test statistic.

b. Find the p-value.

c. Calculate the critical value using α = 0.05

d. What is the conclusion if α = 0.05? Interpret the results at α = 0.05.

e. Calculate the p-value if the above sample mean was based on a sample of 100 observations.

f. Based on a sample of 100 observations, what is the conclusion if α = 0.10? Interpret the results at α = 0.10.

Answer 1