Sample Mean Distribution and T-Interval
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question.docxTitle: 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.
|
|
Bag 1 |
Bag 2 |
Bag 3 |
Bag 4 |
Bag 5 |
|
Student 1 |
3 |
4 |
7 |
6 |
14 |
|
Student 2 |
12 |
14 |
18 |
8 |
3 |
|
Student 3 |
12 |
18 |
8 |
13 |
11 |
|
Student 4 |
18 |
12 |
7 |
11 |
8 |
|
Student 5 |
17 |
18 |
9 |
14 |
2 |
|
Student 6 |
3 |
10 |
14 |
9 |
13 |
|
Student 7 |
3 |
12 |
11 |
9 |
15 |
|
Student 8 |
6 |
2 |
3 |
18 |
11 |
|
Student 9 |
8 |
16 |
12 |
17 |
3 |
|
Student 10 |
14 |
13 |
11 |
17 |
5 |
|
Student 11 |
3 |
14 |
17 |
17 |
15 |
|
Student 12 |
7 |
14 |
11 |
7 |
2 |
|
Student 13 |
17 |
2 |
12 |
18 |
13 |
|
Student 14 |
9 |
18 |
8 |
11 |
10 |
|
Student 15 |
14 |
16 |
4 |
3 |
12 |
|
Student 16 |
4 |
3 |
7 |
11 |
14 |
|
Student 17 |
11 |
17 |
6 |
5 |
13 |
|
Student 18 |
15 |
8 |
17 |
11 |
10 |
|
Student 19 |
4 |
9 |
13 |
16 |
16 |
|
Student 20 |
12 |
12 |
5 |
14 |
16 |
Answer the following questions:
· Find the sample means for each student’s green M&M count.
· Create a histogram of the sample means, and calculate the mean and standard deviation of the sample 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 the frequencies (relative frequencies, percents).
· III. For each class, construct a vertical bar whose height equals the frequency (relative frequency, percent) of that class.
· IV. Label the bars with the classes, the horizontal axis with the name of the variable, and the vertical axis with “Frequency” (“Relative frequency,” “Percent”).
Source: Weiss, Neil A. (2012). Elementary Statistics (8th ed.). Upper Saddle River, NJ: Pearson.
· Theoretically, what are the mean, standard deviation, and distribution of all possible sample means for 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 on the diamond’s weight, color, and clarity. A simple random sample of 18 one-half-carat diamonds had the following prices, in dollars:
|
1676 |
1442 |
1995 |
1718 |
1826 |
2071 |
1947 |
1983 |
2146 |
|
1995 |
1876 |
2032 |
1988 |
2071 |
2234 |
2108 |
1941 |
2316 |
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.
