Purpose: To explore the sampling distribution for sampleproportions.

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 youchoose. You may want to purchase at least a king size package toensure you end up with a sample size that is “large enough.” Selecta color whose proportion you are interested in exploring in thecandy 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 toidentify what the company claims the proportion of your selectedcolor to be for the candy you have chosen. Provide the link for theinternet source you used. The proportion of M&M'S MilkChocolate that are brown is 0.13 according tohttps://blogs.sas.com/content/iml/2017/02/20/proportion-of-colors-mandms.html

Calculate the proportion of your candies that are the color youhave selected. The proportion of my sample of 250 M&M'S MilkChocolate that are brown is 0.6.

Compare your sample proportion to the company’s claim. Do youthink the true population proportion is different from thecompany’s claim? Write the null and alternative hypotheses youwould use to investigate the answer to that question. Writethem in symbolic notation AND write each hypothesis statement in asentence.

Step 2: Check the conditions for normality. Check the conditionsand assumptions necessary to use the normal model as anapproximation for the sampling distribution you are exploring. Showyour work and verify whether you have met the criteria necessary toproceed. (Hint: If your sample size is not large enough, increaseyour sample size!) Remember there are three conditions youneed to check.

Step 3: Use your sample evidence to test your hypotheses.Make a sketch of your sampling distribution. Label the meanand standard deviation (SE), marking at least two SE in eachdirection. Mark your sample proportion in the sketch and shadeappropriately. Complete the hypothesis test using a significancelevel of 5% and analyze your results. Show all of yourwork!

Step 4: State your conclusion. What was the result of yourhypothesis test? Give your final decision AND provide aninterpretation in the context of this problem. Include allimportant details.

Step 5: Confidence Interval Now that you have tested thecompany’s claim and have come to some conclusion about it, you maybe wondering, what really is the true portion of all these candiesthat are the color I chose? Create a 95% confidenceinterval to help you answer that question.Show all of yourwork!

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