Question

16. In the large-scale study conducted by the company in #15, one of the questions asked was how far an employee had to drive to get to work. At that time the average commute distance was 11.3 mi and the standard deviation was 3.86 mi. Although the standard deviation has probably remained pretty much the same, it is believed that the average commute distance has changed, again due to the change in the demographics of the area. To test this conjecture, a sample of 35 employees is taken and the mean commute distance in the sample was 10.1 mi. Do these results indicate a significant change in the average distance an employee of this company drives to work? nl H: work to find p-value: Conclusion: What type of error are you in danger of having made? Type ! Type II

Answer 1

X ~ N(10.1, 3.86)

The hypothesis being tested is:

H₀: µ = 11.3

H_a: µ ≠ 11.3

The test statistic, z = (x - µ)/σ/√n

z = (10.1 - 11.3)/3.86/√35

z = -1.84

The p-value is 0.0659.

Since the p-value (0.0659) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that µ ≠ 11.3.

Type II