Question

It is advertised that the average braking distance for a small car traveling at 70 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 35 small cars at 70 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.

Answer 1

Solution:

Hypothesis are

H0 : = 120

Ha : 120

Test statistic z = = [111- 120]/[21/35] = -2.535

Test statistic = -2.535

Now ,

Here , TWO  tailed test

p value = P(Z < -2.535) + P(Z > +2.535) = 0.0056 + 0.0056 = 0.0112

p value = 0.0112

Decision at = 0.05

Reject H₀ . There is sufficient evidence to support the claim that the statement made in the advertisement is false.

(because p value is less than 0.05 )

Decision at = 0.01

Fail to Reject H₀ . There is not sufficient evidence to support the claim that the statement made in the advertisement is false.

(because p value is greater than 0.05 )