It is advertised that the average braking distance for a small car traveling at 75 miles per hour equals 124 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 37 small cars at 75 miles per hour and records the braking distance. The sample average braking distance is computed as 112 feet. Assume that the population standard deviation is 22 feet. (You may find it useful to reference the appropriate table: z table or t table) a. State the null and the alternative hypotheses for the test.
H0: μ = 124; HA: μ ≠ 124
H0: μ ≥ 124; HA: μ < 124
H0: μ ≤ 124; HA: μ > 124
b. Calculate the value of the test statistic and the p-value. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
Test statistic:
c. Find the p-value.
0.01 p-value < 0.025
0.025 p-value < 0.05
0.05 p-value < 0.10
p-value 0.10
p-value < 0.01
d. Use α = 0.01 to determine if the average breaking distance differs from 124 feet.
The average breaking distance is from 124 feet.
not significantly different | significantly different