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 37 small cars at 65 miles per hour and records the braking distance. The sample average braking distance is computed as 111 feet. Assume that the population standard deviation is 21 feet.
a. State the null and the alternative hypotheses for the test.
b. Calculate the value of the test statistic and the p-value.
c. Use α = 0.01 to determine if the average breaking distance differs from 120 feet.
d. Repeat the test with the critical value approach.