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; H_A: μ ≠ 120

• H₀: μ ≥ 120; H_A: μ < 120

• H₀: μ ≤ 120; H_A: 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

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 tests drives n = 38 small cars at 75 miles per hour and records the braking distance. The sample average braking distance is computed as = 112 feet. Assuming that the population standard deviation is = 20 feet.

a) Hypotheses

So, based on the given claim the hypotheses are:

Ho: μ = 120;

HA: μ ≠ 120

Thus based on the hypothesis, it will be a two-tailed test. Also, the population standard deviation is known and the sample size is greater than 30 hence Z-score is applicable for hypothesis testing.

b) Test Statistic:

P-value:

The P-value is computed using excel formula for normal distribution which takes the calculated Z score as a parameter, thus the formula used is =2*(1-NORM.S.DIST(ABS(-2.466), TRUE)), thus the P-value computed as:

P-value = 0.0137.

0.05 < p-value < 0.10

Rejection region:

At 0.10 level of significance reject Ho if P-value < 0.10

c) Conclusion:

Since P-value is less than 0.10 hence we reject the null hypothesis and conclude that there is enough evidence to support the claim that the average breaking distance differs from 120 feet.