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# Mean Number of Candies in Bag

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Use the M&Ms® data to complete this assignment. You will be using the methods of 7.4 for the color proportions and 7.2 for the mean number of candies per bag. For the Bonus you will be using the methods of 7.5.

You can use StatCrunch to assist with the calculations. A link for StatCrunch can be found under Tools for Success in Course Home. Here is also a link:

http://statcrunch.pearsoncmg.com/statcrunch/larson_les4e/dataset/index.html.

You can also find additional help on both confidence intervals and StatCrunch in the Online Math Workshop under Tab: "MAT300 Archived Workshops". Specifically you will be looking for Hypothesis Tests and Using Technology - Hypothesis Testing.

Submit your answers in Excel, Word or pdf format. Submit your file through the M&M® project link in the weekly course content. Be sure to state clear hypotheses, test statistic values, critical value or p-value, decision (reject/fail to reject), and conclusion in English (what does reject/fail to reject the null mean in terms of your hypotheses). When doing calculations for the color proportions, keep at least 4-6 decimal places sample proportions, otherwise you will encounter large rounding errors.

Masterfoods USA states that their color blends were selected by conducting consumer preference tests, which indicated the assortment of colors that pleased the greatest number of people and created the most attractive overall effect. On average, they claim the following percentages of colors for M&Ms® milk chocolate candies: 24% blue, 20% orange, 16% green, 14% yellow, 13% red and 13% brown.

3 pts. Test their claim that the true proportion of blue M&Ms® candies is 0.24 at the 0.05 significance level.

3 pts. Test their claim that the true proportion of orange M&Ms® candies is 0.20 at the 0.05 significance level.

3 pts. Test their claim that the true proportion of green M&Ms® candies is 0.16 at the 0.05 significance level.

3 pts. Test their claim that the true proportion of yellow M&Ms® candies is 0.14 at the 0.05 significance level.

3 pts. Test their claim that the true proportion of red M&Ms® candies is 0.13 at the 0.05 significance level.

3 pts. Test their claim that the true proportion of brown M&Ms® candies is 0.13 at the 0.05 significance level.

3 pts. On average, they claim that a 1.69 oz bag will contain more than 54 candies. Test this claim (µ > 54) at the 0.01 significance (σ unknown).

BONUS: It is important that the total number of candies per bag does not vary very much. As a result of this quality control, the desired standard deviation is 1.5. Test the claim (α = 0.05) that the true standard deviation for number of candies per 1.69 oz bag is less than 1.5 (σ < 1.5).

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#### Solution Preview

I have attached an Excel Workbook and a Word document describing how to solve these problems.

Here are calculations for the blue M&M's. You can use this and follow the same steps to do the hypothesis tests for the other M&M colors

Let be the unknown population proportion.

The estimate of is the sample proportion .

0.210 (Where 801, and 3819)

The null and alternative hypotheses:

0.24
0.24

The test statistic:

-4.378 ( 0.210, 0.24, and 3819)

If the null hypothesis is true, the observed value of the test statistic, -4.378, is a randomly selected observation from a standard normal distribution.

The rejection region:

The critical values of the rejection region are 1.960 and -1.960 (the 2.5th and the 97.5th ...

#### Solution Summary

The solution determines the mean number of candies in the bag.

\$2.19