Case- Inferential Statistics: Transmission Failure Data Analysis Background: A c

ID: 3325184 • Letter: C

Question

Case- Inferential Statistics: Transmission Failure Data Analysis

Background: A consumer research company looked at customer satisfaction with performance to automobiles produced by one major Detroit manufacturer. A questionnaire sent to owners of one of the manufacturer’s full-sized cars revealed several complaints about EARLY transmission problems. To learn more about transmission failures, the research company gathered some sample of actual transmission repairs provided by a transmission repair firm in the Detroit area where they did note the amount of mileage on the transmission when it came in for repair.

Part 5: Test a claim. If the manufacturer of the transmission claims that their transmissions should last at least 72,000 miles prior to needing any repair. So we want to test whether they last LESS THAN that claimed figure appropriately using alpha=.05. (show all steps in a formal presentation of the hypothesis test solution including the test statistic calculated by hand/formula).

STEP 0: What assumptions are being made in order for these results to be valid

STEP 1: STATE both Ho and Ha and make sure a parameter symbol is in each one (proper parameter symbol).

STEP 2: state alpha level

STEP 3: Calculate the Test statistic by FORMULA in this part (yes, showing all work) and also use your appropriate calculator function to find the correct p-value and state here as well.

STEP 4: Give the decision (Reject Ho and Fail to Reject Ho (aka: Retain Ho) and give support (compare the p-value to the alpha level as your support).

STEP 5: Give the conclusion (sentence form in proper format) , make sure alpha level is given in the beginning of that sentence.

Mileage Data:

25066 32464 32534 32609 35662 37831 39323 40001 53402 53500 59465 59817 59902 61978 63436 64090 64342 64544 65605 66998 67202 67998 69568 69922 72069 73341 74276 74425 77098 77437 77539 79294 82256 85092 85288 85586 85861 86813 88798 89341 89641 92857 94219 95774 101769 116269 116803 118444 121352 138114

Explanation / Answer

X- u

(X-u)^2

25066

-48274.3

2330408040

32464

-40876.3

1670871902

32534

-40806.3

1665154120

32609

-40731.3

1659038800

35662

-37678.3

1419654291

37831

-35509.3

1260910386

39323

-34017.3

1157176699

40001

-33339.3

1111508924

53402

-19938.3

397535806.9

53500

-19840.3

393637504.1

59465

-13875.3

192523950.1

59817

-13523.3

182879642.9

59902

-13438.3

180587906.9

61978

-11362.3

129101861.3

63436

-9904.3

98095158.49

64090

-9250.3

85568050.09

64342

-8998.3

80969402.89

64544

-8796.3

77374893.69

65605

-7735.3

59834866.09

66998

-6342.3

40224769.29

67202

-6138.3

37678726.89

67998

-5342.3

28540169.29

69568

-3772.3

14230247.29

69922

-3418.3

11684774.89

72069

-1271.3

1616203.69

73341

0.7

0.49

74276

935.7

875534.49

74425

1084.7

1176574.09

77098

3757.7

14120309.29

77437

4096.7

16782950.89

77539

4198.7

17629081.69

79294

5953.7

35446543.69

82256

8915.7

79489706.49

85092

11751.7

138102452.9

85288

11947.7

142747535.3

85586

12245.7

149957168.5

85861

12520.7

156767928.5

86813

13472.7

181513645.3

88798

15457.7

238940489.3

89341

16000.7

256022400.5

89641

16300.7

265712820.5

92857

19516.7

380901578.9

94219

20878.7

435920113.7

95774

22433.7

503270895.7

101769

28428.7

808190983.7

116269

42928.7

1842873284

116803

43462.7

1889006291

118444

45103.7

2034343754

121352

48011.7

2305123337

138114

64773.7

4195632212

From Column1 mean = Total / 50 = 3667015/50 = 73340.3

Variance = Column3 total / 50 = 607547093.8

Std. deviation = sq.rt(607547093.8) = 24648.47

Population mean = 72000

H0: transmissions should last at least 72,000 miles prior to needing any repair

Ha: transmissions should be less than 72,000 miles prior to needing any repair

Z= (73340.3 – 72000)/ (24648.47/sq.rt(50))

Z = 0.38

Select alpha = 0.05 Thus, Z = 1.96

P(Z>0.38) = 0.352

As P value is greater than 0.05 (alpha level) we fail to reject null hypothesis or we accept null hypothesis