Project #36546 - Statistics

ask 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.

page1image4816
page1image6904   page1image7792 page1image8384

Bag 1

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Bag 2

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Bag 3

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Bag 4

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Bag 5

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Student 1

3

4

7

6

14

Student 2

12

14

18

8

3

Student 3

12

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18

8

13

11

Student 4

18

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12

7

11

8

Student 5

17

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18

9

14

2

Student 6

3

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10

14

9

13

Student 7

3

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12

11

9

15

Student 8

6

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2

3

18

11

Student 9

8

16

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12

page1image77520

17

page1image79240

3

Student 10

14

13

11

17

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5

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Student 11

3

14

17

17

15

Student 12

7

14

page1image96112 page1image96536

11

page1image98088

7

page1image99808

2

Student 13

17

2

12

18

13

Student 14

9

18

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8

page1image111800

11

page1image113520

10

Student 15

14

16

4

3

12

Student 16

4

3

7

11

14

Student 17

11

17

6

page1image130904

5

page1image132128

13

Student 18

15

8

17

page1image139224

11

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page1image140944

10

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Student 19

4

9

13

16

16

Student 20

12

12

5

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14

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16

Answer the following questions:
a.
Find the sample means for each student’s green M&M count.

1

page1image158984 page1image159144 page1image159304 page1image159464 page1image159624

 

MA3110: Module 3 Sampling Distribution and Confidence Interval Exercise 3.2 Sample Mean Distribution and T-Interval

  1. 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:

    1. Obtain a frequency (relative-frequency, percent) distribution of the data.

    2. Draw a horizontal axis on which to place the bars and a vertical axis on which to display the

      frequencies (relative frequencies, percents).

    3. For each class, construct a vertical bar whose height equals the frequency (relative

      frequency, percent) of that class.

    4. 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.

  2. 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:

Based on the above information, solve the following problems:

  1. 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: x $1964.7 and s $206.5.)

    Obtain a normal probability plot, a boxplot, a histogram, and a stem-and-leaf diagram of the data.

  2. 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. 

Subject Mathematics
Due By (Pacific Time) 07/29/2014 12:00 am
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