MAT 300 M&Ms Project Part 4

MAT 300

 

M&Ms® Project

 

Part 4

   

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: 5 pts. 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).

   

HELP:

 

Color proportions

 

Revisiting the purple example from before: we had found 732 purple candies out of 3500 total candies. The sample proportion of purple candies is 732/3500 = 0.2091428571. Now let’s say you want to test that the true proportion of purple candies is 21% (0.21). First define your hypotheses: Claim – p = 0.21H0: p = 0.21 (null)H1: p ≠ 0.21 (alternative)

   

Next we need to calculate the test statistic. For this type of test, it is a z and a two tailed test. You have been asked to test at alpha = 0.05, so we will reject the null if the test statistic, z, is positive and greater than 1.96 OR if the test statistic, z, is negative and smaller than -1.96. (NOTE: This is the same as if the absolute value of the test statistic is greater than 1.96.)