MA3110: Module 3 Sampling Distribution and Confidence IntervalExercise 3.2Sample Mean Distribution and T-Interval1Task 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’sand asked to count the number of green M&M’s. The results are shown below. The population mean is for abag of this size is 10.06 and the population standard deviation is 2.59.Bag 1 Bag 2 Bag 3 Bag 4 Bag 5Student 1 3 4 7 6 14Student 2 12 14 18 8 3Student 3 12 18 8 13 11Student 4 18 12 7 11 8Student 5 17 18 9 14 2Student 6 3 10 14 9 13Student 7 3 12 11 9 15Student 8 6 2 3 18 11Student 9 8 16 12 17 3Student 10 14 13 11 17 5Student 11 3 14 17 17 15Student 12 7 14 11 7 2Student 13 17 2 12 18 13Student 14 9 18 8 11 10Student 15 14 16 4 3 12Student 16 4 3 7 11 14Student 17 11 17 6 5 13Student 18 15 8 17 11 10Student 19 4 9 13 16 16Student 20 12 12 5 14 16Answer the following questions:a. Find the sample means for each student’s green M&M count.MA3110: Module 3 Sampling Distribution and Confidence IntervalExercise 3.2Sample Mean Distribution and T-Interval2b. Create a histogram of the sample means, and calculate the mean and standard deviation of thesample means. To construct a histogram, follow the given steps:I. Obtain a frequency (relative-frequency, percent) distribution of the data.II. Draw a horizontal axis on which to place the bars and a vertical axis on which to display thefrequencies (relative frequencies, percents).III. For each class, construct a vertical bar whose height equals the frequency (relativefrequency, percent) of that class.IV. Label the bars with the classes, the horizontal axis with the name of the variable, and thevertical axis with “Frequency” (“Relative frequency,” “Percent”). Source: Weiss, Neil A. (2014: 2024 – Essay Writing Service. Custom Essay Services Cheap). Elementary Statistics (8th ed.). Upper Saddle River, NJ: Pearson.c. Theoretically, what are the mean, standard deviation, and distribution of all possible sample meansfor a sample size of 5?Task 2: Read the following case study, titled “Diamond Pricing”:In a Singapore Edition of Business Times, diamond pricing was explored. The price of a diamond is based onthe diamond’s weight, color, and clarity. A simple random sample of 18 one-half-carat diamonds had thefollowing prices, in dollars:1676 1442 1995 1718 1826 2071 1947 1983 21461995 1876 2032 1988 2071 2234 2108 1941 2316Based on the above information, solve the following problems:a. Apply the t-interval procedure to these data to find a 90% confidence interval for the mean price ofall one-half-carat diamonds. Interpret your result. (Note:x . s . . ? ? $1964 7 and $206 5)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 inpart a? Explain your answer.MA3110: Module 3 Sampling Distribution and Confidence IntervalExercise 3.2Sample Mean Distribution and T-Interval3Submission Requirements:? Submit the assignment in a Microsoft Word or Excel document.? Show detailed steps and provide appropriate rationale with your answers.Evaluation Criteria:? Correctly answered each question? Included appropriate steps or rationale to determine the answer to each question

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