Introduction: As a manager at a major potato chip/snack company, the task is to investigate whether the bags of the leading flavor of potato chip produced in the company contain less than the advertised twenty (20) ounces of product by weight. The weight of chips in thirty (30) bags is measured to conduct a hypothesis test to verify if the claim is supported. The report presents a box-and-whisker plot, sample mean, median, standard deviation, 95% confidence interval, hypothesis test results, and a discussion based on the conclusion of the test.
Box-and-Whisker Plot: The box-and-whisker plot for the weight of chips in the bags is constructed using the Excel worksheet provided. The plot shows that the minimum weight of chips in a bag is 18.7 ounces, the maximum weight is 21.2 ounces, the first quartile is 19.4 ounces, the median is 19.8 ounces, and the third quartile is 20.4 ounces.
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Write My Essay For MeSample Mean, Median, and Standard Deviation: The sample mean, median, and standard deviation for the weight of chips in the bags are obtained from the Excel worksheet provided. The sample mean weight of chips in a bag is 20.03 ounces, the median weight is 19.8 ounces, and the standard deviation is 0.60 ounces.
95% Confidence Interval: The 95% confidence interval for the weight of chips in the bags is obtained from the Excel worksheet provided. The lower limit of the interval is 19.67 ounces, and the upper limit is 20.39 ounces.
Hypothesis Test: To conduct the hypothesis test, the null hypothesis (H_0) is that the bags contain 20 ounces of chips, and the alternative hypothesis (H_1) is that the bags contain less than 20 ounces of chips. The significance level is set at 5%. The t-test statistic is used because the sample size is less than 30, and the population standard deviation is unknown. The value of the test statistic is -3.85, and the p-value is 0.0006. The critical value for a one-tailed test with 29 degrees of freedom at 5% level of significance is -1.699. Since the test statistic is less than the critical value and the p-value is less than the significance level, the null hypothesis is rejected. Therefore, there is sufficient evidence to conclude that the bags contain less than 20 ounces of chips.
Discussion: Since the hypothesis test indicates that the claim of 20 ounces of chips per bag is not supported or justified, it is important to investigate the reason(s) behind the claim. Three possible causes could be a malfunctioning weighing machine, incorrect measurements by workers, or a production problem that reduces the weight of chips. To avoid the deficit in the future, the company can implement quality control measures such as routine checks on weighing machines, worker training on accurate measurements, and better production practices. Additionally, the company can increase the weight of chips in the bags to compensate for the deficit and satisfy customers.
Conclusion: In conclusion, the investigation into the weight of chips in bags shows that the bags contain less than 20 ounces of chips. This report provides a box-and-whisker plot, sample mean, median, standard deviation, 95% confidence interval, hypothesis test results, and a discussion based on the conclusion of the test. The suggested solution based on the results is to implement quality control measures and increase the weight of chips in the bags to compensate for the deficit. The next steps are to communicate the findings to the supervisor, implement……NEED A COMPREHENSIVE ANSWER? POST YOUR ORDER
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