EXERCISE 3.2 | Complete Solution

EXERCISE 3.2 (3.5 hours)

Assessment Preparation Checklist:

To prepare for this assessment:

    Read Chapters 7 and 8 from your textbook, Elementary Statistics. These readings examine concepts such as The Sampling Distribution of the Sampling Mean and Confidence Intervals for the One Population Mean.

Study the topics “The Mean and Standard Deviation of Sample Mean” and “Estimating a Population Mean” in the Module 3 lesson. These topics will help you learn how to calculate the mean and standard deviations of the sample mean and estimate a population mean.

Title: Sample Mean Distribution and T-Interval

Task 1: Read the following case study, titled “Green M&M’s”:

Green M&M’s: Consider a class of 20 statistics students, where each student is given 5 small bags of M&M’s and asked to count the number of green M&M’s. The results are shown below. The population mean is for a bag of this size is 10.06 and the population standard deviation is 2.59.

Based on the above information, solve the following problems:

    Apply the t-interval procedure to these data to find a 90% confidence interval for the mean price of all one-half-carat diamonds. Interpret your result. (Note: ) Obtain a normal probability plot, a boxplot, a histogram, and a stem-and-leaf diagram of the data.
    b. Based on your graphs from part (b), is it reasonable to apply the t-interval procedure as you did in part a? Explain your answer.