Question

It is advertised that the average braking distance for a small car traveling at 75 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 38 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 20 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 = 120; HA: μ ≠ 120 H0: μ ≥ 120; HA: μ < 120 H0: μ ≤ 120; HA: μ > 120 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.) Find the p-value. 0.025 p-value < 0.05 0.05 p-value < 0.10 p-value 0.10 p-value < 0.01 0.01 p-value < 0.025 c. Use α = 0.10 to determine if the average breaking distance differs from 120 feet.

Answer 1

This is the two tailed test .

The null and alternative hypothesis is

H₀ : = 120

H_a : 120

Test statistic = z

= ( - ) /    / n

= (112 - 120) / 20 / 38

Test statistic = -2.47

P-value = 0.0137

0.01 < p-value < 0.025

P-value < = 0.10

Reject the null hypothesis .

There is sufficient evidence to conclude that the average braking distance for a small car traveling at 75 miles per hour equals 120 feet