Question
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 15:053/7 12:422.90069On time214
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Eastern3/4 16:50**Back order500
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Central3/4 8:463/6 16:562.34028On time307
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Central3/4 9:413/10 17:136.31389Late59
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Central3/4 10:073/6 16:132.25417On time174
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Central3/4 10:293/8 10:374.00556On time146
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Central3/4 11:103/8 17:204.25694On time334
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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
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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
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Central3/4 14:433/7 8:402.74792On time416
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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
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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
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Central3/4 16:183/9 8:074.65903On time191
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Central3/4 16:29**Back order346
Central3/4 16:393/9 10:384.74931On time32
Western3/4 8:223/7 15:003.27639On time252
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Western3/4 9:443/7 10:083.01667On time291
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Western3/4 15:423/6 9:121.72917On time446
Western3/4 15:463/7 14:232.94236On time322
Western3/4 15:503/6 13:091.88819On time438
Western3/4 15:513/7 9:302.73542On time124
Western3/4 15:563/5 16:421.03194On time389
Western3/4 16:003/8 9:233.72431On time230
Western3/4 16:083/7 11:562.82500On time286
Western3/4 16:103/10 8:305.68056On time217
Western3/4 16:123/6 8:211.67292On time265
Western3/4 16:153/7 10:052.74306On time199
Western3/4 16:1818203/6 9:201.70833On time228
Western3/4 16:263/7 11:342.79722On time278
Western3/4 16:323/8 9:573.72569On time473
Western3/4 16:39**Back order279
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