Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
9th Edition
ISBN: 9781319013387
Author: David S. Moore, George P. McCabe, Bruce A. Craig
Publisher: W. H. Freeman
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Chapter 6.1, Problem 5UYK

(a)

To determine

To graph: A diagram with the use of confidence interval applet.

(a)

Expert Solution
Check Mark

Explanation of Solution

Calculation: To construct confidence inetrvals, use confidence interval applet. The following steps are provided below:

Step 1: Go to the “Confidence interval applets” in the website. The screenshot is

shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  1

Step 2: Specify confidence interval as “80” and specify the sample size as “20.” The screenshot is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  2

Step 3: Click on the “Sample 25” to generate the sample. The screenshot is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  3

Graph: The obtained output is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  4

From the above srceenshot, intervals that contain the true mean μ will be colored gray and “misses” will be colored as red.

Interpretation: From the above output, out of a total 25, 21 intervals contain the true mean and the proportion of the interval that contains true mean is 84%.

(b)

To determine

To find: The confidence interval with 50 SRSs.

(b)

Expert Solution
Check Mark

Answer to Problem 5UYK

Solution: The confidence interval with 50 SRSs is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  5

Explanation of Solution

Calculation: To construct confidence intervals, use confidence interval applet. The following steps are provided below:

Step 1: Go to the “Confidence interval applets” in the website. The screenshot is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  6

Step 2: Specify confidence interval as “80” and specify the sample size as “20.” The screenshot is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  7

Step 3: Click twice on the “Sample 25” to generate the sample. The screenshot is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  8

The obtained output is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  9

From the above sceenshort, intervals that contain the true mean μ will be colored gray and “misses” will be colored as red.

Interpretation: The above figure indicates the hit 35, total 50, and percent hit 70%. Thirty-five out of 50 intervals contain the true mean and the proportion of the interval that contains the true mean is 70%.

To determine

To find: The confidence interval with 100 SRSs.

Expert Solution
Check Mark

Answer to Problem 5UYK

Solution: The confidence interval with 100 SRSs is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  10

Explanation of Solution

Calculation: To construct confidence inetrvals, use confidence interval applet. The following steps are provided below:

Step 1: Go to the “Confidence interval applets” in the website. The screenshot is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  11

Step 2: Specify confidence interval as “80” and specify the sample size as “20.” The screenshot is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  12

Step 3: Click four times on the “Sample 25” to generate the sample. The screenshot is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  13

The obtained output is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  14

From the above sceenshort, intervals that contain the true mean μ will be colored gray and “misses” will be colored as red.

Interpretation: The above figure indicates the hit 75, total 100, and percent hit 75%. Seventy-five out of 100 intervals contain the true mean and the proportion of the interval that contains the true mean is 75%.

To determine

To find: The confidence interval with 200 SRSs.

Expert Solution
Check Mark

Answer to Problem 5UYK

Solution: The confidence interval with 200 SRSs is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  15

Explanation of Solution

Calculation: To construct confidence inetrvals, use confidence interval applet. The following steps are provided below:

Step 1: Go to the “Confidence interval applets” in the website. The screenshot is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  16

Step 2: Specify confidence interval as “80” and specify the sample size as “20.” The screenshot is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  17

Step 3: Click eight times on the “Sample 25” to generate the sample. The screenshot is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  18

The obtained output is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  19

From the above sceenshort, intervals that contain the true mean μ will be colored gray and “misses” will be colored as red.

Interpretation: The above figure indicates the hit 157, total 200, and percent hit 79%. One hundred and fifty-seven out of 200 intervals contain the true mean and the proportion of the interval that contains the true mean is 79%.

To determine

To find: The confidence interval with 300 SRSs.

Expert Solution
Check Mark

Answer to Problem 5UYK

Solution: The confidence interval with 300 SRSs is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  20

Explanation of Solution

Calculation: To construct confidence inetrvals, use confidence interval applet. The following steps are provided below:

Step 1: Go to the “Confidence interval applets” in the website. The screenshot is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  21

Step 2: Specify confidence interval as “80” and specify the sample size as “20.” The screenshot is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  22

Step 3: Click 12 times on the “Sample 25” to generate the sample. The screenshot is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  23

The obtained output is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  24

From the above sceenshort, intervals that contain the true mean μ will be colored gray and “misses” will be colored as red.

Interpretation: The above figure indicates the hit 232, total 300, and percent hit 77%. Two hundred and thirty-two out of 300 intervals contain the true mean and the proportion of the interval that contains the true mean is 77%.

To determine

To find: The confidence interval with 400 SRSs.

Expert Solution
Check Mark

Answer to Problem 5UYK

Solution: The confidence interval with 400 SRSs is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  25

Explanation of Solution

Calculation: To construct confidence inetrvals, use confidence interval applet. The following steps are provided below:

Step 1: Go to the “Confidence interval applets” in the website. The screenshot is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  26

Step 2: Specify confidence interval as “80” and specify the sample size as “20.” The screenshot is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  27

Step 3: Click 16 times on the “Sample 25” to generate the sample. The screenshot is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  28

The obtained output is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  29

From the above sceenshort, intervals that contain the true mean μ will be colored gray and “misses” will be colored as red.

Interpretation: The above figure indicates the hit 315, total 400, and percent hit 79%. Three hundred and fifteen out of 400 intervals contain the true mean and the proportion of the interval that contains the true mean is 79%.

To determine

To find: The confidence interval with 500 SRSs.

Expert Solution
Check Mark

Answer to Problem 5UYK

Solution: The confidence interval with 500 SRSs is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  30

Explanation of Solution

Calculation: To construct confidence inetrvals, use confidence interval applet. The following steps are provided below:

Step 1: Go to the “Confidence interval applets” in the website. The screenshot is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  31

Step 2: Specify confidence interval as “80” and specify the sample size as “20.” The screenshot is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  32

Step 3: Click 20 on the “Sample 25” to generate the sample. The screenshot is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  33

The obtained output is shown below:

Introduction to the Practice of Statistics, Chapter 6.1, Problem 5UYK , additional homework tip  34

From the above sceenshort, intervals that contain the true mean μ will be colored gray and “misses” will be colored as red.

Interpretation: The above figure indicates the hit 397, total 500, and percent hit 79%. Three hundred and ninety-seven out of 500 intervals contain the true mean and the proportion of the interval that contains the true mean is 79%. From the pattern in the above seven cases, the proportion hit approaches near by 80% as the number of sample increases. Thus, one should expect that the percent capture to get closer to the confidence interval level is 80% as the number of samples increases.

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Chapter 6 Solutions

Introduction to the Practice of Statistics

Ch. 6.1 - Prob. 11UYKCh. 6.1 - Prob. 12ECh. 6.1 - Prob. 13ECh. 6.1 - Prob. 14ECh. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Prob. 21ECh. 6.1 - Prob. 22ECh. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.1 - Prob. 25ECh. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - Prob. 28ECh. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - Prob. 32ECh. 6.1 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.1 - Prob. 36ECh. 6.1 - Prob. 37ECh. 6.2 - Prob. 38UYKCh. 6.2 - Prob. 39UYKCh. 6.2 - Prob. 40UYKCh. 6.2 - Prob. 41UYKCh. 6.2 - Prob. 42UYKCh. 6.2 - Prob. 43UYKCh. 6.2 - Prob. 44UYKCh. 6.2 - Prob. 45UYKCh. 6.2 - Prob. 46UYKCh. 6.2 - Prob. 47UYKCh. 6.2 - Prob. 48UYKCh. 6.2 - Prob. 49UYKCh. 6.2 - Prob. 50UYKCh. 6.2 - Prob. 51UYKCh. 6.2 - Prob. 52ECh. 6.2 - Prob. 53ECh. 6.2 - Prob. 54ECh. 6.2 - Prob. 55ECh. 6.2 - Prob. 56ECh. 6.2 - Prob. 57ECh. 6.2 - Prob. 58ECh. 6.2 - Prob. 59ECh. 6.2 - Prob. 60ECh. 6.2 - Prob. 61ECh. 6.2 - Prob. 62ECh. 6.2 - Prob. 63ECh. 6.2 - Prob. 64ECh. 6.2 - Prob. 65ECh. 6.2 - Prob. 66ECh. 6.2 - Prob. 67ECh. 6.2 - Prob. 68ECh. 6.2 - Prob. 69ECh. 6.2 - Prob. 70ECh. 6.2 - Prob. 71ECh. 6.2 - Prob. 72ECh. 6.2 - Prob. 73ECh. 6.2 - Prob. 74ECh. 6.2 - Prob. 75ECh. 6.2 - Prob. 76ECh. 6.2 - Prob. 77ECh. 6.2 - Prob. 78ECh. 6.2 - Prob. 79ECh. 6.2 - Prob. 80ECh. 6.2 - Prob. 81ECh. 6.2 - Prob. 82ECh. 6.2 - Prob. 83ECh. 6.2 - Prob. 84ECh. 6.2 - Prob. 85ECh. 6.2 - Prob. 86ECh. 6.2 - Prob. 87ECh. 6.2 - Prob. 88ECh. 6.2 - Prob. 89ECh. 6.3 - Prob. 90UYKCh. 6.3 - Prob. 91UYKCh. 6.3 - Prob. 92ECh. 6.3 - Prob. 93ECh. 6.3 - Prob. 94ECh. 6.3 - Prob. 95ECh. 6.3 - Prob. 96ECh. 6.3 - Prob. 97ECh. 6.3 - Prob. 98ECh. 6.3 - Prob. 99ECh. 6.3 - Prob. 100ECh. 6.3 - Prob. 101ECh. 6.3 - Prob. 102ECh. 6.3 - Prob. 103ECh. 6.3 - Prob. 104ECh. 6.3 - Prob. 105ECh. 6.3 - Prob. 106ECh. 6.3 - Prob. 107ECh. 6.3 - Prob. 108ECh. 6.3 - Prob. 109ECh. 6.4 - Prob. 110ECh. 6.4 - Prob. 111ECh. 6.4 - Prob. 112ECh. 6.4 - Prob. 113ECh. 6.4 - Prob. 114ECh. 6.4 - Prob. 115ECh. 6.4 - Prob. 116ECh. 6.4 - Prob. 117ECh. 6.4 - Prob. 118ECh. 6.4 - Prob. 119ECh. 6.4 - Prob. 120ECh. 6.4 - Prob. 121ECh. 6.4 - Prob. 122ECh. 6.4 - Prob. 123ECh. 6 - Prob. 124ECh. 6 - Prob. 125ECh. 6 - Prob. 126ECh. 6 - Prob. 127ECh. 6 - Prob. 128ECh. 6 - Prob. 129ECh. 6 - Prob. 130ECh. 6 - Prob. 131ECh. 6 - Prob. 132ECh. 6 - Prob. 133ECh. 6 - Prob. 134ECh. 6 - Prob. 135ECh. 6 - Prob. 136ECh. 6 - Prob. 137ECh. 6 - Prob. 138ECh. 6 - Prob. 139ECh. 6 - Prob. 140ECh. 6 - Prob. 141ECh. 6 - Prob. 142ECh. 6 - Prob. 143ECh. 6 - Prob. 144E
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