Module 8 Question 13: Jensen Tire & Auto is in the process of deciding whether t

Question

Module 8 Question 13: Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computer wheel alignment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars).

a. Develop the estimated regression equation that relates annual maintenance expense (in hundreds of dollars) to weekly usage hours (to 3 decimals).

Expense = ___ + ___ Weekly Usage

b. Test the significance of the relationship in part (a) at a .05 level of significance.

-Compute the value of the F test statistic (to 2 decimals).

-The p value is -less than .01 or between .01 and .025 or between .025 and .05 or between .05 and .10 or greater than .10?

-What is your conclusion?

c. Jensen expects the new machine to be used 30 hours per week. What is the expected annual maintenance expense in hundreds of dollars (to 2 decimals)?

Develop a 95% prediction interval for the company's annual maintenance expense for this machine (to 2 decimals).
( ___ , ___ )

d. If the maintenance contract costs $3000 per year, would you recommend purchasing the contract for the new machine in part (c)?

Weekly Usage
(hours) Annual
Maintenance Expense 16 23 13 28 23 36 31 43 35 53 20 37 27 39 34 45 43 58 41 46

Explanation / Answer

a. Develop the estimated regression equation that relates annual maintenance expense (in hundreds of dollars) to weekly usage hours (to 3 decimals).

Ans: The regression equation is
Expense = 13.7 + 0.956 Weekly_Usage

b. Test the significance of the relationship in part (a) at a .05 level of significance.

Ans:

Analysis of Variance

Source DF SS MS F P
Regression 1 864.92 864.92 45.92 0.000
Residual Error 8 150.68 18.83
Total 9 1015.60

The estimated p-value is less than 0.05 level of significance. Hence, Weekly_Usage has significant association with expenses at 0.05 level of significance.

-The p value is -less than .01 or between .01 and .025 or between .025 and .05 or between .05 and .10 or greater than .10?

Ans: p-value is less than 0.01

-What is your conclusion?

Ans:  The estimated p-value is less than 0.01 level of significance. Hence, Weekly_Usage has significant association with expenses at 0.01 level of significance.

c. Jensen expects the new machine to be used 30 hours per week. What is the expected annual maintenance expense in hundreds of dollars (to 2 decimals)?

Ans: The expected annual maintenance expense in hundreds of dollars when Jensen expects the new machine to be used 30 hours per week is

Expense = 13.7 + 0.956*30=42.38

Develop a 95% prediction interval for the company's annual maintenance expense for this machine (to 2 decimals).

Ans:

( 4.64 , 24.76 )

d. If the maintenance contract costs $3000 per year, would you recommend purchasing the contract for the new machine in part (c)?

Ans:  If the maintenance contract costs $3000 per year, I would not recommend purchasing the contract for the new machine in part (c).

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