Question

(Round all intermediate calculations to at least 4 decimal places.) 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 36 small cars at 120 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 20 feet. Use Table 1. 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 values should be indicated by a minus sign. Round "Test statistics" to 2 decimal places. Round "p-value" to 4 decimal places.) Test statistics p-value The p-value is: 0.01 Picture p-value < 0.025 0.025 Picture p-value < 0.05 0.05 Picture p-value < 0.10 p-value Picture 0.10 p-value < 0.01 c. Use α = 0.01 to determine if the average breaking distance differs from 120 feet. The average breaking distance is different from 120 miles. d. Repeat the test with the critical value approach. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.) Critical values are and and we H0.

Answer 1

(a)
Correct option:
H0: = 120; HA: 120

(b)
SE = /

= 20/ = 3.3333

Test statistic is:
Z = (111 - 120)/3.3333 = - 2.70

So,

Test statistic is:

Z = - 2.70

(c)
Table of Area Under Standard Normal Curve gives area = 0.4965

So,

P- Value = (0.5 - 0.4965) X 2 = 0.0070

So,

Correct option:

P - Value < 0.025
Since P - value = 0.0070 is less than = 0.01, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that the average breaking distance is different from 120 miles.

(d)

= 0.01

From Table, critical values of Z = 2.576

Since the calculated value of Z = - 2.70 is less than critical value of Z = - 2.576, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that the average breaking distance is different from 120 miles.