Suppose you buy a case of 36 cans of soda and carefully measure the volume of each. You average the results and determine that the sample mean is 12.1 oz. Let’s assume that you know that the canning facility outputs cans whose volumes are distributed normally with a standard deviation of 0.24 oz. What is the 80% confidence interval of the mean of the volume? Is it larger or smaller than the 90% confidence interval. Does this make sense?

A

Since z* is equal to 1.282 for the 80% confidence interval, the 80% confidence interval of the mean of the volume is 12.1 ± 1.282 × (0.24 / (36 0.5)) = 12.1 ± 0.05128. It can be stated that the calculated interval is smaller than the 90% confidence interval, with z* being equal to 1.645. That is why it does not make sense to use the 80% confidence interval as it captures the population mean only for 80% of all possible samples. One may note that it would be more feasible to use the 90% or 95% confidence interval.

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Academic.Tips. (2021) 'Suppose you buy a case of 36 cans of soda and carefully measure the volume of each. You average the results and determine that the sample mean is 12.1 oz. Let's assume that you know that the canning facility outputs cans whose volumes are distributed normally with a standard deviation of 0.24 oz. What is the 80% confidence interval of the mean of the volume? Is it larger or smaller than the 90% confidence interval. Does this make sense'. 25 September.

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Academic.Tips. (2021, September 25). Suppose you buy a case of 36 cans of soda and carefully measure the volume of each. You average the results and determine that the sample mean is 12.1 oz. Let's assume that you know that the canning facility outputs cans whose volumes are distributed normally with a standard deviation of 0.24 oz. What is the 80% confidence interval of the mean of the volume? Is it larger or smaller than the 90% confidence interval. Does this make sense? Retrieved from https://academic.tips/question/suppose-you-buy-a-case-of-36-cans-of-soda-and-carefully-measure-the-volume-of-each-you-average-the-results-and-determine-that-the-sample-mean-is-12-1-oz-lets-assume-that-you-know-that-the-canning/

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Academic.Tips. 2021. "Suppose you buy a case of 36 cans of soda and carefully measure the volume of each. You average the results and determine that the sample mean is 12.1 oz. Let's assume that you know that the canning facility outputs cans whose volumes are distributed normally with a standard deviation of 0.24 oz. What is the 80% confidence interval of the mean of the volume? Is it larger or smaller than the 90% confidence interval. Does this make sense?" September 25, 2021. https://academic.tips/question/suppose-you-buy-a-case-of-36-cans-of-soda-and-carefully-measure-the-volume-of-each-you-average-the-results-and-determine-that-the-sample-mean-is-12-1-oz-lets-assume-that-you-know-that-the-canning/.

1. Academic.Tips. "Suppose you buy a case of 36 cans of soda and carefully measure the volume of each. You average the results and determine that the sample mean is 12.1 oz. Let's assume that you know that the canning facility outputs cans whose volumes are distributed normally with a standard deviation of 0.24 oz. What is the 80% confidence interval of the mean of the volume? Is it larger or smaller than the 90% confidence interval. Does this make sense?" September 25, 2021. https://academic.tips/question/suppose-you-buy-a-case-of-36-cans-of-soda-and-carefully-measure-the-volume-of-each-you-average-the-results-and-determine-that-the-sample-mean-is-12-1-oz-lets-assume-that-you-know-that-the-canning/.


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Academic.Tips. "Suppose you buy a case of 36 cans of soda and carefully measure the volume of each. You average the results and determine that the sample mean is 12.1 oz. Let's assume that you know that the canning facility outputs cans whose volumes are distributed normally with a standard deviation of 0.24 oz. What is the 80% confidence interval of the mean of the volume? Is it larger or smaller than the 90% confidence interval. Does this make sense?" September 25, 2021. https://academic.tips/question/suppose-you-buy-a-case-of-36-cans-of-soda-and-carefully-measure-the-volume-of-each-you-average-the-results-and-determine-that-the-sample-mean-is-12-1-oz-lets-assume-that-you-know-that-the-canning/.

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"Suppose you buy a case of 36 cans of soda and carefully measure the volume of each. You average the results and determine that the sample mean is 12.1 oz. Let's assume that you know that the canning facility outputs cans whose volumes are distributed normally with a standard deviation of 0.24 oz. What is the 80% confidence interval of the mean of the volume? Is it larger or smaller than the 90% confidence interval. Does this make sense?" Academic.Tips, 25 Sept. 2021, academic.tips/question/suppose-you-buy-a-case-of-36-cans-of-soda-and-carefully-measure-the-volume-of-each-you-average-the-results-and-determine-that-the-sample-mean-is-12-1-oz-lets-assume-that-you-know-that-the-canning/.

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