Question

It is advertised that the average braking distance for a small car traveling at 70 miles per hour equals 122 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 33 small cars at 70 miles per hour and records the braking distance. The sample average braking distance is computed as 115 feet. Assume that the population standard deviation is 24 feet.

a. State the null and the alternative hypotheses for the test. Choose one of the three options below.

H0: μ = 122; HA: μ ≠ 122

H0: μ ≥ 122; HA: μ < 122

H0: μ ≤ 122; HA: μ > 122

b. Calculate the value of the test statistic and the p-value.

Find the p-value. p-value 0.10 p-value < 0.01 0.01 p-value < 0.025 0.025 p-value < 0.05 0.05 p-value < 0.10

c. Use α = 0.10 to determine if the average breaking distance differs from 122 feet.

Answer 1

Here we have: X = 115 0 = 24 n = 33 a = 0.10 Hypothesis: Ho; u = 122 Hai Ml 122 Test statistics: z-distribution (o known) χ-μ z= = 115-122 24 33 = -1.68 vn

P-value = 2p (Z > -1.681) = 0.0930 0.05 < P-value <0.10 Reject the null hypothesis. Conclusion: Here we have sufficient evidence to reject the null hypothesis. P- value is less than alpha value. We can support the claim that the breaking distance differs from 122 feet