final project update

Introductory Statistics Design the Study 1. List the Group Members with Both First and Last Names: Angie Anderson, Robin Correa, Maryn McMurdie, Katlin Howes, Rebekah Preston, Mike Chapman, Joshua Hamilton, and Marcella Velazquez.  2. Explain the purpose of your study. We are trying to determine whether the average M&M bag (of 1.69 oz.) is or is not equal to 50 individual M&M pieces. Our group has eight members. We will compile the names of the randomly selected stores from the different states to buy the 1.69 oz. bags of M&M’s. Each member of the group will buy five bags (1.69 oz. each) of M&M’s from their randomly selected store. The total of selected bags will give us a sample size of 40 bags of the 1.69 oz. size. Each member will count and record the number of M&M's they find in each of their five bags. Each member will update their data in the group Excel sheet. 3. Determine whether this be a Designed Experiment or an Observational Study. Explain. This is an observational study because we are not trying to influence the results but rather merely observe how Many M&Ms are in a 1.69 oz. bag. 4. Identify the response variable(s). (Tip: carefully consider what you are going to observe and record) Determine whether the response variable is numeric or categorical. (Lesson 2 Section 4.4) The response variable is the amount of M&Ms in each 1.69 oz. bag. 5. Identify the population. 40 1.69 oz. bags of M&Ms.  6. Identify the population parameter of interest. The population parameter of interest is the population mean. 7. State your Null and Alternative Hypothesis in words and symbols. Ho: µ = 50 M&M’s Ha: µ ≠ 50 M&M’s µ: The population mean of the number of M&M’s in a 1.69 oz bag of M&M’s.  8. State and Define your Planned Sampling Method. (Lesson 2 Section 4.3) The quantitative, one sample, sigma unknown has two requirements: 1. The data represents a simple sample from the population. Our group randomly selected stores to buy the 1.69 oz. bags of M&Ms from the different states in the USA.  2. The Distribution of the sample mean is normal. Our simple random sample contains a large number of 40. According to the Central Limit Theorem, if the sample size is (n>30) the mean is normally distributed.  9. How will you apply the planned sampling method? Our group has eight members. We will compile the names of the randomly selected stores from the different states to buy the 1.69 oz. bags of M&M’s. Each member of the group will buy five bags (1.69

oz. each) of M&M’s from their randomly selected store. The total of selected bags will give us a sample size of 40 bags of the 1.69 oz. size. Each member will count and record the number of M&M's they find in each of their five bags. Each member will update their data in the group Excel sheet. 10. Explanation of why you chose this type of method. We felt like this sampling would give an accurate representation because it came from a random sample and we planned on collecting 40 1.69 oz. bags of M&Ms which is large. Collect the Data 1. What did you learn in Data collection? We learned that collecting the data would be relatively easy, as all of our group mates were willing to participate, and the size of M&M’s bag we chose was also easy to find at stores across the United States. 2. Describe how sampling was completed. A cluster sample consists of taking all items in one or more randomly selected clusters or blocks. We instructed our group members to go to a random store near them and collect the 5 bags of M&M’s. Therefore, our data is from several different kinds of stores all around the United States. The locations l and stores were Walmart (Idaho), 7-Eleven and Five Below (Texas), Gerbs (Missouri), Dollar General (North Carolina), Kroger (Kentucky), Publix (Florida), and Walmart (Arizona). 3. Describe things you did not anticipate. We did not anticipate that the data we collected would be consistently greater than the 50 advertised by the M&M brand.   4. List the Sample Sizes Gathered by Group. We collected 40 total bags of M&M’s. Describe the Data 1. Provide Numerical Summaries.   The sample Mean is equal to 56.013 The sample Standard deviation is equal to 1.763 

55 10 (25%) 56 4 (10%) 57 10 (25%) 57.5 1 (2.5%) 58 4 (10%) 59 2 (5%) 60 1 (2.5%) Name of group member Store where you bought M&Ms State you bought them in Count of M&Ms per bag (1.69oz) Angie Dollar General North Carolina 57, 57. 57, 58, 55 Rebekah Gerbs Missouri 55,56,55,57,56 Kate Walmart ☀ Idaho 57,59,55,59,58 Josh Kroger Kentucky 54, 53, 54, 54, 54 Mike Walmart Arizona 55, 52, 56, 57, 54 Robin Publix Florida 57, 57, 55, 55, 54 Marcella 7-Eleven Texas 60, 57.5, 58, 57, 58 Maryn Five-Below Texas 55, 56, 55, 55, 57 3. Make a statement comparing the groups or the one group to the null hypothesis based on your numerical and graphical summaries. The sample mean (56.013) appears to be above the null hypothesis (μ = 50). Make Inference 1. Describe the method used and why you used the method. 2. Check the requirements of the statistical method. 3. State the null and alternative hypotheses in words and symbols. 4. State the level of significance. 5. State the test statistics and degrees of freedom. 6. State the p-value. 7. Make a statement on rejecting or not rejecting the null hypothesis by comparing the p- value to the level of significance.

8. Make a concluding statement and reference the alternative hypothesis when making the concluding statement. 9. Calculate and interpret the confidence interval. 10. Compare the confidence interval to the null hypothesis to determine whether the null hypothesis should be rejected. Take Action 1. What action item would you take given the results you obtained?