Claim of the True Proportion of Blue M&Ms Candies

See attached file.

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.

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.

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

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

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

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

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

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

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 (Ï? unknown).

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 (? = 0.05) that the true standard deviation for number of candies per 1.69 oz bag is less than 1.5 (Ï? < 1.5).

At the end of this project, you will be writing a report, explaining the method and presenting the results from each part of the project. You might find it useful to write this as you complete the work, so the report will be mostly written by the time it is assigned.