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Confidence interval and t-tests for M&M's claims

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Comparing Two Population Means

In 2004, the Mars Candy Company stated on their Web site that their 1.69 oz. package of M&M's contained an average of at least 53 candies and that 14% of all M&Ms manufactured were yellow. Students in a Math 1040 statistics class at the Salt Lake Community College were asked to determine if these two claims were true or not true.

It's now 2013. We would like to know if the claims made in 2004 are true or not true today. Fifteen packages of 1.69 oz. M&M's have been obtained from various cities around the United States.

Utilizing the data contained in the "WA4_M&Ms" Excel file and using the Excel statistical functions and formulas do the following:
"WA4_M&Ms" see file is attached

1. Calculate the mean and standard deviation for the average number of M&M's in a package.

2. Find the 99% confidence interval for the population mean.

3. Perform a hypothesis test relative to the claim that each package contains an average of at least 53 M&Ms.

4. Calculate the minimum sample size for testing this claim using a maximum error of the estimate of 1.

5. Document your data analysis and conclusion such that someone not educated in statistics can read, understand,
and agree or disagree with your stated result.

6. Calculate the proportion of yellow M&Ms contained in all of the packages.

7. Find the 95% confidence interval of the true proportion of yellow M&Ms in a 1.69 oz. package.

8. Perform a hypothesis test relative to the claim that 14% of all M&M's manufactured by the Mars Candy Company
are yellow.

9. Calculate the minimum sample size for testing this claim using a maximum error of the estimate of 3%.

10. Document your data analysis and conclusion such that someone not educated in statistics can read,
understand, and agree or disagree with your stated result.

Submit all Excel output including tables, function formulas, charts, and graphs with the rationale for your conclusions.

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Solution Summary

The solution provides detailed steps to compute the confidence interval, to conduct the t-tests, and to compute the sample size. It also draws conclusion based on the test results and provides explanation.

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