The owner of an auto repair shop hires an accountant to estimate the cost functi
ID: 3234383 • Letter: T
Question
The owner of an auto repair shop hires an accountant to estimate the cost function for estimating weekly overhead costs (Y) based on the repair hours (X) done at the shop. The data set is given below. You can copy and paste the data into an Excel file for doing your calculations. Answer the questions below and be sure to show your work.
X
Repair Hours
Y
Overhead Costs
231
9514
231
8867
463
12823
267
10178
183
8677
363
10285
551
12506
327
9968
431
10840
527
12892
323
10453
395
12230
367
10494
387
12439
195
8087
At a 0.05 level of significance, test the significance of the linear relationship by using an F test.
List the formula for the FSTAT. FSTAT = __________________________
Estimate the FSTAT for this problem. FSTAT = _________________________
List the degrees of freedom. Numerator df1 = ____ Denominator df2 = ____
List the critical F value. F = _______
List the decision rule. _______________________________________________________
_________________________________________________________________________
Do you accept or reject the null hypothesis?__________
What is your conclusion? At the 0.05 level of significance, is there a significant relationship between overhead costs and repair hours? ____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
X
Repair Hours
Y
Overhead Costs
231
9514
231
8867
463
12823
267
10178
183
8677
363
10285
551
12506
327
9968
431
10840
527
12892
323
10453
395
12230
367
10494
387
12439
195
8087
Explanation / Answer
1) FSTAT = MSTR/MSE
2) The table below gives the calculations
FSTAT = 87.33878
3) Degrees of freedom: df1 = 1, df2 = 40
4) The critical value: Fcv0.05,1,40 = 4.0847
5) The decision rule: If Fstat is > Fcv, Then Reject H0.
6) Since FSTAT(87.33) is > Fcv(4.0847), Hence we reject H0.
7) There is sufficient evidence at the 95% level of significance to conclude that there isn't a significant relationship between repair hours and overhead costs.
Source Sum of sq DF Mean Square F Between 1061892354.90 1 1061892354.9 87.33878 Within 486332595.45 40 12158314.89 Total 1548224950.35 41Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.