Capstone Part $4$: Final Report

Present your analysis and key findings in a formal report to the production manager. The report should be well$-$organized, state the problem or issue identified through the analysis, state the actions or steps taken to address the issue and the results of those actions, and end with recommended next steps. Do some creative thinking and research to develop your recommendations; include some lower cost solutions along with more expensive solutions.

Statements should be supported by your data analysis$$remember$,$ numbers convince! Be selective in your choice of descriptive statistics you include in the report; do not include all of them. Likewise, when reporting the results of a hypothesis test, simply tell the findings, indicate the level of significance, and perhaps include the p$-$value. Management does not need to see all the calculations in the report.

Descriptive Statistic Value Analysis$/$Interpretation

Mean

$583\mathrm{.}5782$ It is interesting to note that the average weight of cereal boxes is $583\mathrm{.}59.$ This information could potentially be used to improve packaging and reduce waste.

Median

$584\mathrm{.}1298$

Based on the data, it appears that the median weight of the wax boxes is $584\mathrm{.}13,$ which is slightly higher than the company's average weight. This could be an opportunity to investigate and optimize the weight of the wax boxes to ensure consistency and efficiency in the production process.

Mode

$583\mathrm{.}056$

The mode of $583\mathrm{.}056$ being close to the mean suggests that many boxes are clustered around a common weight, which is a positive sign for consistency in the packaging process.

Standard Deviation

$8\mathrm{.}764051$

This is a great opportunity to examine weight differences among boxes and determine potential causes for variation.

Range

$54\mathrm{.}7273$

This analysis shows us the difference between the weight of the heaviest object and the weight of the lightest object and tries to identify any patterns or insights that might emerge. This analysis could be useful in identifying trends or factors that contribute to weight variations and could ultimately inform strategies for optimizing weight management

Lowest Value $549\mathrm{.}563$

Upon closer inspection, we can see that the box with the lowest weight is positioned below the company's average weight of $574.$ This could be a cause for concern as it may indicate that the product is not meeting the company's standards. It would be beneficial to investigate the reasons behind the lower weight and find ways to optimize the weight of the products to ensure they meet the company's requirements.

Highest Value $604\mathrm{.}2903$

the highest weight exceeds the company's average weight of $574$g by a considerable margin. The deviation in the weight of the object in question indicates that it may be an outlier or an anomalous item that needs to be further examined to ensure quality control standards are met.

Proportion of boxes below label weight

$65$ boxes With $65$ boxes $(13\%)$ below the label weight, this could indicate a problem with the filling equipment or process that needs to be addressed to ensure compliance with weight regulations.

Proportion of boxes above label weight

$435$ boxes

The fact that $435$ boxes $(87\%)$ are above the label weight suggests that overfilling is more common than underfilling. This could be costly and might warrant a review of the filling process to reduce overfilling.

Proportion of boxes below MAV

$545$

The proportion of $545$ boxes below the MAV might indicate a compliance issue with weight regulations, and management should take steps to ensure that the minimum weight is consistently met.

Skewness $-0\mathrm{.}49912$

The skewness value of $-0\mathrm{.}49912$ indicates a slight leftward skew, meaning there are more boxes on the lower end of the weight scale. This could suggest that the packaging process might be erring on the side of underfilling rather than overfilling.

$2.$ Using Excel, create and insert a frequency distribution and histogram of the box weights. Use the $2$k $>=$ n rule to determine how many classes to include in the frequency distribution.

Weight Frequency

$555\mathrm{.}64382$

$561\mathrm{.}72468$

$567\mathrm{.}805416$

$573\mathrm{.}886231$

$579\mathrm{.}967112$

$586\mathrm{.}0478127$

$592\mathrm{.}1286127$

$598\mathrm{.}209458$

$604\mathrm{.}290319$

$3.$ Based on the descriptive statistics, the histogram, and the empirical rule, does it appear that the box weights follow a normal distribution with a symmetrical, bell$-$shaped curve? Justify your response with your data analysis.

Regarding the histogram and frequency distribution, if the histogram shows a symmetrical bell$-$shaped curve and the majority of the data falls within three standard deviations of the mean, it would suggest that the box weights follow a normal distribution. The empirical rule states that for a normal distribution, approximately $68\%$ of data falls within one standard deviation, $95\%$ within two standard deviations, and $99\mathrm{.}7\%$ within three standard deviations of the mean. If the histogra