Question

Exercise 9-22 Algo 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 34 small cars at 65 miles per hour and records the braking distance. The sample average braking distance is computed as 116 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 = 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. p-value < 0.01 0.01 p-value < 0.025 0.025 p-value < 0.05 0.05 p-value < 0.10 p-value 0.10

c. Use α = 0.05 to determine if the average breaking distance differs from 120 feet.

Answer 1

Here the random sample size(n) = 34

Sample Average (x̄) = 116 feet

Population standard deviation(σ) = 22 feet

It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet

Therefore, μ0 = 120 feet

a. Null and alternative hypothesis are-

H0: μ = 120; HA: μ ≠ 120

b. Test statistic Z is given as-

p value = 2.P(Z<-1.06) = 2.P(1-0.8554) (from table)

=  .2891

c. Significance level = 0.05

p value > significance level (α = 0.05)

Hence, we can accept the null hypothesis that the mean is equal to 120.

z table-