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Please see below for the worksheets that go along with this homework Data Analysis Assignment 3 The Normal Distribution and Confidence Intervals (Chapters 6, 7

Please see below for the worksheets that go along with this homework

Data Analysis Assignment 3

The Normal Distribution and Confidence Intervals (Chapters 6, 7 and 8)

An engineer who is responsible for a cereal packaging line records the fill weights of 100 cereal boxes. The results are found in the Minitab worksheet CerealBoxWeight.MTW. Open the worksheet.

1.Using Minitab, calculate the mean and standard deviation for the data set. Copy and paste your Minitab results below.

2.Assume that the weight of cereal boxes is normally distributed. Use Minitab and the mean and standard deviation that you found above to calculate the probability that a randomly selected cereal box weighs less than 87 grams. Copy and paste your distribution plot below.

3.The engineer pulls one cereal box off of the packaging line and finds that it weighs 87 grams. Would you consider this to be unusual? Explain.

4.Use Minitab and the mean and standard deviation that you found above to calculate the probability that a simple random sample of 10 cereal boxes has a mean weight 87 grams or less. Copy and paste your distribution plot below.

5.The engineer pulls ten cereal boxes off of the packaging line and finds that they have a mean weight of 87 grams. Would you consider this to be unusual? Explain.

An economist wants to determine whether the monthly energy cost for families has changed from the previous year, when the mean cost per month was $200. The economist randomly samples 25 families and records their energy costs for the current year. The results are found in the Minitab worksheet FamilyEnergyCost.MTW. Open the worksheet.

6. Using Minitab, calculate the sample mean and sample standard deviation for the data set (column C2). Copy and paste your Minitab results below.

7.Use the results above to calculate a 95% confidence interval for the mean monthly energy cost. Copy and paste your Minitab results below.

8.Did you use Z, t, or proportion to calculate the confidence interval? Explain why.

9.Based on your results above, do you think that the mean cost per month has changed from the previous year (when it was $200)? Explain.

10.The economist wants to conduct a larger study to determine the monthly energy cost for families. Find the sample size necessary to estimate the mean monthly energy cost for families such that it can be said with 95% confidence that the sample mean is within $10 of the true mean. Assume that the population standard deviation is $154. Show your work.

A scientist for a company that manufactures processed food wants to assess the percentage of fat in the company's bottled sauce. The advertised percentage is 15%. The scientist measures the percentage of fat in 20 randomly sampled bottles. Previous measurements found that the population standard deviation is 2.6%. The results are found in the Minitab worksheet FatContent.MTW. Open the worksheet.

11. Using Minitab, calculate the sample mean for the data set (column C2). Copy and paste your Minitab results below.

12.Previous measurements found that the population standard deviation is 2.6%. Calculate a 95% confidence interval for the mean percentage of fat in the sauce. Copy and paste your Minitab results below.

13.Did you use Z, t, or proportion to calculate the confidence interval? Explain why.

14.Based on your results above, do you think that the advertised percentage of 15% is accurate? Explain.

15.The scientist wants to take a larger sample to determine the fat content of the sauce. Find the sample size necessary to estimate the mean fat content of the sauce such that it can be said with 95% confidence that the sample mean is within 0.5 percent of the true mean. Recall that the population standard deviation is 2.6%. Show your work.

A company that sells books online records data on shipping time and distance. The company's goal is that 92% of deliveries will be on-time. The records for 319 orders are found in the Minitab worksheet ShippingData.MTW. Open the worksheet.

16.Using Minitab, create frequency distribution table (Tally) for the Status data (column C5). Include both count and percent in your table. Copy and paste your Minitab table below.

17.Calculate a 95% confidence interval for the percent of deliveries that are on time (hint: the number of on-time deliveries in the table above is the number of events).

18.Did you use Z, t, or proportion to calculate the confidence interval? Explain why.

19.Based on your results above, do you think that the company is meeting its goal? Explain.

20.The shipping manager wants to take a larger sample to determine the percentage of on-time deliveries. Find the sample size necessary to estimate the percentage of on-time deliveries with 95% confidence and a margin of error equal to 0.02. Use the value for percentage of on-time deliveries from your frequency distribution table as the value for p from a prior study. Show your work.

To turn in this assignment, go to the Data Analysis Assignment 3 folder on Blackboard. Click on the Data Analysis Assignment 3 submission link at the bottom. Under Assignment Submission, attach both documents (using Browse My Computer). Then click Submit.

Cereal:

Weight

87.3733

87.6280

89.5787

86.2406

89.0082

86.9615

85.9849

88.2681

87.9071

89.4005

90.6034

87.0928

89.6514

86.3376

91.3149

91.8069

91.4675

87.3325

90.7782

88.0996

93.1125

87.9633

89.2366

86.6148

87.3538

89.1797

85.6544

89.1183

91.0487

90.2304

90.6740

86.0346

88.1316

89.1435

89.6264

88.6265

88.2260

92.2772

94.6818

89.2904

87.8025

89.2237

93.6807

89.9277

88.5841

88.9610

87.3810

90.7059

90.7507

87.3246

87.4843

90.3925

88.6041

88.8231

88.5617

85.6946

92.5658

91.9003

90.7597

88.6491

91.3526

88.5597

85.3914

91.2417

89.8051

90.7000

87.1533

86.9523

88.7118

89.3473

90.0891

90.0344

86.7787

89.0366

89.7867

87.0693

86.9654

89.3474

85.0787

89.0842

88.3829

90.4522

90.7555

88.0614

87.1100

86.3953

91.2455

89.7673

91.1821

91.5548

85.2667

88.9175

91.7175

84.1766

89.4420

88.2067

89.8107

87.9076

87.9112

93.3748

Family IDEnergy Cost

1211

2572

3558

4250

5478

6307

7184

8435

9460

10308

11188

12111

13676

14326

15142

16255

17205

1877

19190

20320

21407

22333

23488

24374

25409

Fat Content

Sample IDPercent Fat

115.2

212.4

315.4

416.5

515.9

617.1

716.9

814.3

919.1

1018.2

1118.5

1216.3

1320.0

1419.2

1512.3

1612.8

1717.9

1816.3

1918.7

2016.2

Center OrderArrival DaysStatus Distance

Eastern3/4 8:343/8 15:214.28264On time255

Eastern3/4 8:353/7 17:053.35417On time196

Eastern3/4 8:38**Back order299

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Eastern3/4 13:563/9 16:305.10694On time90

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Eastern3/4 14:153/10 8:135.74861On time231

Eastern3/4 14:183/9 8:134.74653On time348

Eastern3/4 14:293/6 11:071.85972On time197

Eastern3/4 14:303/7 8:122.73750On time265

Eastern3/4 14:413/8 15:044.01597On time333

Eastern3/4 14:50**Back order224

Eastern3/4 14:533/10 13:465.95347On time307

Eastern3/4 14:573/9 8:564.74931On time146

Eastern3/4 15:053/7 12:422.90069On time214

Eastern3/4 15:113/9 9:064.74653On time126

Eastern3/4 15:163/8 8:563.73611On time170

Eastern3/4 15:193/8 9:113.74444On time333

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Eastern3/4 15:363/9 9:264.74306On time364

Eastern3/4 15:433/7 16:073.01667On time368

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Eastern3/4 15:513/9 9:314.73611On time286

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Eastern3/4 16:043/9 9:084.71111On time190

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Eastern3/4 16:393/9 10:344.74653On time423

Eastern3/4 16:433/9 10:394.74722On time441

Eastern3/4 16:50**Back order500

Eastern3/4 16:563/9 11:104.75972On time243

Central3/4 8:463/6 16:562.34028On time307

Central3/4 8:523/7 15:123.26389On time340

Central3/4 8:553/8 15:104.26042On time327

Central3/4 8:583/7 14:593.25069On time81

Central3/4 9:043/9 10:125.04722On time235

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Central3/4 9:093/9 10:145.04514On time226

Central3/4 9:113/7 15:463.27431On time312

Central3/4 9:143/7 15:173.25208On time184

Central3/4 9:163/9 11:375.09792On time145

Central3/4 9:213/10 8:565.98264On time348

Central3/4 9:26**Back order232

Central3/4 9:303/9 15:415.25764On time386

Central3/4 9:343/9 16:095.27431On time246

Central3/4 9:343/9 10:475.05069On time265

Central3/4 9:413/10 17:136.31389Late59

Central3/4 9:443/7 9:172.98125On time306

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Central3/4 9:573/6 15:592.25139On time484

Central3/4 10:073/6 16:132.25417On time174

Central3/4 10:093/6 12:182.08958On time500

Central3/4 10:133/8 17:184.29514On time230

Central3/4 10:183/6 16:492.27153On time315

Central3/4 10:193/6 12:572.10972On time208

Central3/4 10:253/7 16:463.26458On time159

Central3/4 10:293/8 10:374.00556On time146

Central3/4 10:413/8 17:064.26736On time94

Central3/4 10:453/8 16:494.25278On time271

Central3/4 10:483/8 16:564.25556On time181

Central3/4 10:513/7 10:042.96736On time201

Central3/4 10:543/6 17:192.26736On time228

Central3/4 10:553/9 17:185.26597On time255

Central3/4 10:583/6 13:492.11875On time54

Central3/4 11:013/7 15:143.17569On time360

Central3/4 11:053/11 12:467.07014Late498

Central3/4 11:083/9 17:265.26250On time380

Central3/4 11:103/8 17:204.25694On time334

Central3/4 11:153/5 17:401.26736On time242

Central3/4 11:213/7 17:353.25972On time123

Central3/4 11:263/8 11:073.98681On time315

Central3/4 11:32**Back order105

Central3/4 11:353/6 12:462.04931On time284

Central3/4 11:373/7 9:142.90069On time376

Central3/4 11:393/9 12:465.04653On time161

Central3/4 11:493/8 16:004.17431On time264

Central3/4 11:513/8 9:063.88542On time312

Central3/4 11:533/8 13:044.04931On time252

Central3/4 11:543/8 10:493.95486On time196

Central3/4 0:00**Back order268

Central3/4 11:563/8 11:083.96667On time267

Central3/4 12:003/7 9:462.90694On time106

Central3/4 12:023/9 10:024.91667On time357

Central3/4 12:063/10 8:565.86806On time154

Central3/4 12:083/6 14:322.10000On time333

Central3/4 12:133/8 15:404.14375On time270

Central3/4 12:173/6 8:091.82778On time363

Central3/4 12:223/8 13:344.05000On time314

Central3/4 12:233/7 8:512.85278On time228

Central3/4 12:293/9 11:194.95139On time208

Central3/4 12:373/8 17:234.19861On time284

Central3/4 12:433/8 13:414.04028On time328

Central3/4 12:493/6 15:462.12292On time187

Central3/4 12:52**Back order364

Central3/4 12:593/8 11:373.94306On time224

Central3/4 13:023/9 16:455.15486On time175

Central3/4 13:053/8 14:174.05000On time265

Central3/4 13:083/10 16:006.11944Late110

Central3/4 13:103/9 15:385.10278On time395

Central3/4 13:163/8 8:093.78681On time52

Central3/4 13:173/10 10:015.86389On time276

Central3/4 13:303/8 9:353.83681On time312

Central3/4 13:343/6 8:161.77917On time394

Central3/4 13:413/9 13:084.97708On time370

Central3/4 13:503/7 12:022.92500On time229

Central3/4 13:553/10 12:595.96111On time334

Central3/4 14:033/8 8:023.74931On time269

Central3/4 14:073/10 16:006.07847Late179

Central3/4 14:103/7 16:243.09306On time354

Central3/4 14:163/8 9:323.80278On time433

Central3/4 14:243/6 8:181.74583On time157

Central3/4 14:303/6 8:001.72917On time329

Central3/4 14:323/8 12:093.90069On time185

Central3/4 14:433/7 8:402.74792On time416

Central3/4 14:543/8 8:223.72778On time266

Central3/4 14:593/8 8:563.74792On time165

Central3/4 15:083/7 13:202.92500On time59

Central3/4 15:113/8 8:533.73750On time298

Central3/4 15:133/10 9:045.74375On time188

Central3/4 15:223/8 9:023.73611On time294

Central3/4 15:263/11 8:286.70972Late187

Central3/4 15:29**Back order96

Central3/4 15:323/10 13:465.92639On time260

Central3/4 15:373/9 9:094.73056On time319

Central3/4 15:423/9 8:374.70486On time210

Central3/4 15:483/8 16:074.01319On time357

Central3/4 15:543/9 9:284.73194On time261

Central3/4 16:023/7 9:362.73194On time221

Central3/4 16:083/8 8:493.69514On time274

Central3/4 16:113/8 9:573.74028On time182

Central3/4 16:143/9 10:064.74444On time182

Central3/4 16:183/9 8:074.65903On time191

Central3/4 16:223/8 10:203.74861On time98

Central3/4 16:29**Back order346

Central3/4 16:393/9 10:384.74931On time32

Western3/4 8:223/7 15:003.27639On time252

Western3/4 8:303/6 16:302.33333On time259

Western3/4 8:423/7 17:303.36667On time227

Western3/4 8:453/5 15:451.29167On time303

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Western3/4 9:443/7 10:083.01667On time291

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Western3/4 9:50**Back order346

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Western3/4 11:24**Back order97

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