Sample Mean Distribution and T-Interval

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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.

 

 

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.

 


 

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