Question

Purpose: To explore the sampling distribution for sample proportions.

Materials: One package of candies with multiple colors (M&M’s – any variety, Skittles – any variety, Reese’s Pieces, etc.). You may select any size package but be mindful of the “sample size” which will vary depending on the type of candy you choose. You may want to purchase at least a king size package to ensure you end up with a sample size that is “large enough.” Select a color whose proportion you are interested in exploring in the candy you have chosen.

I have chosen the following candy: M&M'S Milk Chocolate

I have selected the following color: Brown

Step 1: Identify your hypotheses. Do some internet research to identify what the company claims the proportion of your selected color to be for the candy you have chosen. Provide the link for the internet source you used. The proportion of M&M'S Milk Chocolate that are brown is 0.13 according to https://blogs.sas.com/content/iml/2017/02/20/proportion-of-colors-mandms.html

Calculate the proportion of your candies that are the color you have selected. The proportion of my sample of 250 M&M'S Milk Chocolate that are brown is 0.6.

Compare your sample proportion to the company’s claim. Do you think the true population proportion is different from the company’s claim? Write the null and alternative hypotheses you would use to investigate the answer to that question. Write them in symbolic notation AND write each hypothesis statement in a sentence.

Step 2: Check the conditions for normality. Check the conditions and assumptions necessary to use the normal model as an approximation for the sampling distribution you are exploring. Show your work and verify whether you have met the criteria necessary to proceed. (Hint: If your sample size is not large enough, increase your sample size!) Remember there are three conditions you need to check.

Step 3: Use your sample evidence to test your hypotheses. Make a sketch of your sampling distribution. Label the mean and standard deviation (SE), marking at least two SE in each direction. Mark your sample proportion in the sketch and shade appropriately. Complete the hypothesis test using a significance level of 5% and analyze your results. Show all of your work!

Step 4: State your conclusion. What was the result of your hypothesis test? Give your final decision AND provide an interpretation in the context of this problem. Include all important details.

Step 5: Confidence Interval Now that you have tested the company’s claim and have come to some conclusion about it, you may be wondering, what really is the true portion of all these candies that are the color I chose? Create a 95% confidence interval to help you answer that question.Show all of your work!

Step 6: Write a sentence to describe the meaning of your confidence interval in the context of this problem. How does the interval you calculated compare to the company’s claim? Does it support the company’s claim or give evidence against it? How does this compare with the results of your hypothesis test?

Answer 1