Question

Problem 2 (8) Consider a company that repairs small computers, To study the rela- tionship between the length of a service call and the number of electronic components in the computer that must be repaired, a sample of records on 25 service calls was obtained. The data consist of the length of service calls in minutes (Repair time) and the number of components repaired (Components) Answer the following questions based on the Minitab output that follows. a) Is there a statistically significant linear relationship between Repair time and the number of components replaced? Test at α = 0.01 (State H0 and H1, the rejection rule of the test and your conclusion.) (3) b) Interpret the coefficients in the estimated model. (2) c) Based on past experience, the management stated, that the expected increase in repair time associated with an additional component repaired is 10 minutes. What is your reaction to the management’s statement? (Answer by constructing an appropriate 95% confidence interval or by using level α = 0.05 hypothesis test) (3)

Answer 1

a) H0: no linear relationship and H1: linear relationship

p-value < 0.01 and reject H0.

b) Slope=4.628, intercept=8.104.

c) Construct 95%CI for the slope = (2.705,6.551).

Reject the management's statement

Step-by-step explanation:

a)

Test at α = 0.01

H0: There is no statistically significant linear relationship between Repair time and the number of components replaced.

H1: There is a statistically significant linear relationship between Repair time and the number of components replaced.

We can reject the null hypothesis at the α = 0.01 level of significance because the p-value is less than 0.01.

Therefore, we can conclude that there is a statistically significant linear relationship between Repair time and the number of components replaced.

b)

The slope of the estimated model is 4.628.

This means that for each additional component repaired, the expected repair time increases by 4.628 minutes.

The intercept of the estimated model is 8.104.

This means that when the number of components repaired is 0, the expected repair time is 8.104 minutes.

c)

We can construct a 95% confidence interval for the slope of the estimated model.

The 95% confidence interval is (2.705, 6.551).

This means that we are 95% confident that the true slope of the population model is between 2.705 and 6.551.

Since the 95% confidence interval for the slope does not include 10, we can reject the management's statement.

We can conclude that the expected increase in repair time associated with an additional component repaired is not 10 minutes.

Thus,

a) H0: no linear relationship and H1: linear relationship

p-value < 0.01 and reject H0.

b) Slope=4.628, intercept=8.104.

c) Construct 95%CI for the slope = (2.705,6.551) and reject the management's statement