Question

In the automated packaging process, equipment is set to fill boxes with a mean weight of 574 grams. This is the standard for the population. Population standard deviation is not known.

1. Calculate a 95% confidence interval for the mean weight of the cereal boxes, using the sample data given in the Excel spreadsheet labeled Cereal Weights.

2. Based on the confidence interval for the mean weight of cereal boxes, does this sample of 400 boxes provide evidence that the packaging process is meeting the company standard? Explain.

3. The company engineer decided to make adjustments to the filling equipment to correct the issue. A random sample of 30 boxes was selected and weighed after the adjustment. The data for this sample can be found in the Excel spreadsheet labeled Weights after Adjustment. Find the descriptive statistics and the 95% confidence interval for the mean weight of packages after the equipment adjustment. Using the descriptive statistics and the confidence interval, does it appear that the equipment adjustment had any effect on the weight of the packages? Explain.

4. Using the data from the Weights after Adjustment, conduct a hypothesis test, using this sample data, to determine whether the mean weight of cereal boxes is meeting the company standard mean weight 574 grams after the equipment adjustment, with the level of significance of .05. Consider carefully whether a one-tail test or a two-tail test would be more useful to management. Use the company standard mean weight as the population mean; population standard deviation is not known.

Null hypothesis: ____________________________________________________

Alternative hypothesis: ______________________________________________

Critical value: ______________________________________________________

Test statistic: ______________________________________________________ (Must show calculation of test statistic.)

p-value: ___________________________________________________________

Decision: __________________________________________________________

What conclusions can you draw about the population mean weight based on the hypothesis test? Was the equipment adjustment enough to meet the company standard?

589.3672 |

589.3955 |

558.3806 |

579.1045 |

579.1328 |

558.409 |

558.4373 |

561.6692 |

585.1714 |

591.8053 |

561.7259 |

578.9344 |

578.9911 |

588.6017 |

588.7718 |

566.5738 |

593.5346 |

593.563 |

549.5638 |

595.9444 |

587.4677 |

566.6588 |

571.3082 |

587.4963 |

571.6484 |

572.9526 |

592.1171 |

592.3156 |

572.9525 |

572.9809 |

573.0376 |

579.0478 |

585.2281 |

573.4912 |

573.5479 |

573.6046 |

573.8597 |

573.8882 |

581.0039 |

571.5917 |

581.0323 |

573.8883 |

573.8881 |

590.4161 |

573.9731 |

574.3984 |

575.6174 |

576.3829 |

563.7388 |

588.82 |

576.431 |

576.4594 |

576.998 |

577.1114 |

577.0547 |

577.2248 |

577.2815 |

577.4516 |

577.48 |

577.5083 |

587.2325 |

577.5085 |

577.6215 |

591.8818 |

577.6222 |

579.0961 |

586.3535 |

584.6809 |

584.7092 |

577.622 |

577.9619 |

585.1629 |

591.9101 |

580.6835 |

561.8024 |

578.0186 |

587.3458 |

578.2738 |

591.8532 |

578.2738 |

578.8976 |

600.4151 |

579.0392 |

581.9876 |

564.5524 |

584.9927 |

591.9103 |

579.1243 |

590.2376 |

590.2942 |

579.3794 |

571.3564 |

587.6293 |

579.0959 |

579.3227 |

577.5366 |

579.3511 |

585.531 |

579.4078 |

582.4653 |

584.8467 |

579.687 |

577.5324 |

580.7076 |

583.7127 |

577.5891 |

579.6868 |

579.772 |

577.3339 |

579.8287 |

587.9368 |

588.1069 |

579.8572 |

579.9988 |

580.1973 |

566.646 |

580.3107 |

580.3674 |

580.6792 |

580.7643 |

574.3288 |

590.2331 |

574.3572 |

590.2899 |

586.0659 |

599.4753 |

573.4216 |

580.9911 |

581.1895 |

581.2179 |

581.5297 |

588.3621 |

588.4188 |

581.5864 |

581.6148 |

578.2411 |

566.5609 |

593.6352 |

573.3933 |

581.6149 |

581.8699 |

573.0247 |

581.9266 |

585.5273 |

581.9267 |

579.1483 |

581.9551 |

585.0167 |

582.1251 |

582.0071 |

582.1488 |

582.1772 |

588.159 |

588.1874 |

582.2055 |

582.3473 |

582.3756 |

582.404 |

582.4323 |

583.056 |

583.056 |

583.7081 |

587.2235 |

583.7648 |

583.7932 |

586.1462 |

583.8215 |

583.8498 |

583.9349 |

583.9632 |

583.9636 |

583.9631 |

584.3034 |

584.3601 |

590.3136 |

590.342 |

590.3703 |

584.3885 |

584.5302 |

584.5586 |

584.5869 |

584.8421 |

584.5869 |

583.056 |

584.6436 |

584.7287 |

592.4115 |

584.757 |

581.6104 |

584.7854 |

584.8137 |

584.8422 |

585.0122 |

585.0405 |

585.0407 |

585.0687 |

587.7621 |

585.0688 |

585.2107 |

585.2391 |

585.2675 |

585.2677 |

585.2674 |

585.3241 |

593.8292 |

585.5793 |

585.6076 |

576.5923 |

577.1026 |

585.636 |

591.1926 |

591.9013 |

582.0354 |

585.6358 |

581.1567 |

588.9813 |

581.185 |

585.6359 |

585.6361 |

585.6643 |

574.0408 |

574.0692 |

585.6927 |

585.7494 |

585.9478 |

594.8497 |

586.0048 |

586.0045 |

604.2903 |

586.0329 |

586.1179 |

586.1746 |

573.5589 |

586.203 |

577.1593 |

586.2029 |

595.1332 |

586.2031 |

586.3731 |

599.5842 |

600.4914 |

586.3731 |

582.0639 |

586.4014 |

586.4298 |

586.4582 |

574.0978 |

574.4944 |

586.7983 |

586.6667 |

586.6953 |

586.7236 |

586.752 |

587.1772 |

580.6851 |

587.2059 |

591.8833 |

587.2055 |

587.3757 |

587.404 |

587.4324 |

587.4891 |

587.4892 |

592.7906 |

583.7185 |

587.5741 |

583.8603 |

587.6592 |

587.6875 |

578.3037 |

578.8706 |

587.6875 |

587.7159 |

590.5792 |

587.7726 |

588.0277 |

588.1413 |

588.1978 |

581.9892 |

582.1309 |

588.2262 |

583.7752 |

588.453 |

580.2598 |

580.2882 |

588.5099 |

588.5097 |

588.538 |

588.5664 |

588.7932 |

588.9916 |

574.3914 |

575.5537 |

588.9919 |

603.7336 |

589.0483 |

589.0486 |

589.2468 |

589.4615 |

589.4617 |

589.4898 |

566.8382 |

571.4309 |

589.5182 |

589.5749 |

590.2836 |

592.4949 |

590.3403 |

590.3687 |

590.7089 |

594.0542 |

579.0287 |

590.7111 |

590.7656 |

590.7939 |

591.1058 |

591.1625 |

603.7215 |

603.8066 |

591.1625 |

591.9563 |

591.9847 |

582.0905 |

591.9848 |

592.013 |

576.0803 |

576.1086 |

576.5055 |

592.0415 |

592.0413 |

592.1264 |

592.1831 |

575.7684 |

575.8251 |

576.0236 |

592.1832 |

592.1833 |

592.2114 |

592.2398 |

592.4666 |

592.495 |

580.8149 |

592.8068 |

592.8069 |

592.8351 |

592.8635 |

592.8636 |

603.8068 |

603.8349 |

592.7421 |

592.7705 |

592.7707 |

592.7988 |

580.6936 |

592.8272 |

593.5359 |

593.5926 |

583.0181 |

583.0464 |

593.621 |

593.6212 |

593.6496 |

593.6499 |

593.6493 |

593.6777 |

593.706 |

593.7062 |

593.8478 |

593.8761 |

593.9045 |

593.9612 |

594.6132 |

579.8429 |

580.098 |

580.1264 |

594.6418 |

594.6416 |

594.6983 |

594.9818 |

580.2681 |

594.9818 |

595.0385 |

595.0668 |

597.0797 |

571.338 |

571.5363 |

597.1364 |

597.1931 |

579.0779 |

599.4044 |

599.4327 |

600.425 |

600.4533 |

580.7217 |

603.4869 |

603.4868 |

581.147 |

603.5151 |

566.6034 603.7136 |

Answer #1

I used R software to solve this question.

R codes:

weight=scan('clipboard')

Read 400 items

t.test(weight,mu=574)

One Sample t-test

data: weight

t = 25.714, df = 399, p-value < 2.2e-16

alternative hypothesis: true mean is not equal to 574

95 percent confidence interval:

583.8503 585.4812

sample estimates:

mean of x

584.6658

**Que.1**

**95% confidence interval for mean weight of cereal box
is,**

**Lower bound = 583.8503**

**Upper bound = 585.4812**

**Que.2**

**Since 95% confidence interval does not contain value
574, hence we conclude that packaging process does not meet the
company's standard.**

**Please provide data 'Weights after adjustment' for
solving question no.3 and 4.**

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