Elementary Statistics (Text Only)
Elementary Statistics (Text Only)
2nd Edition
ISBN: 9780077836351
Author: Author
Publisher: McGraw Hill
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Chapter 10.3, Problem 13E

(a)

To determine

To construct a 95% confidence, interval for the mean.

(a)

Expert Solution
Check Mark

Answer to Problem 13E

The 95% confidence interval for the mean increase in height for boys between the ages of 12 and 14 is (5.182 inches, 5.5529 inches)

Explanation of Solution

Given information:

Age 12 Age 14 Age 12 Age 14
57.9 62.9 55.4 61.8
61.1 65.9 58.7 64.2
62.7 67.5 64.3 69.8
67.5 73.7 58.1 63.3
59.2 64.9 63.3 69.6
61.4 67 61.2 66.4
60.7 65.5 64.5 69.2
55.9 62.1 55.9 62
59.7 65.4 60.4 65.7
56.3 61.5 57.8 62.8
63 68.5 68.3 73.6
58.6 63.9 63 67.7
61.1 65.8 64.4 69.2
59.5 64.5 58.2 64.6
61.6 66.3 59.7 66.1
59.3 64.2 60.2 65.9
62.1 67.1 63.7 68.3
62.8 68.1 60.2 65.2
65.3 69.9 62.7 67.9
60.4 66.7 55.6 61.73

Formula used Construct the 95% confidence interval for the mean increase in height for boys between the ages of 12 and 14 by using MINITAB.

MINITAB procedure:

Step 1: Choose Stat > Basic Statistics > Paired t

Step 2: In First Sample enter the column of Age 14

Step 3: In Second Sample enter the column of Age 12.

Step 4: Check Options, and enter the Confidence level as 95.0

Step 5: Choose not equal in alternative

Step 6: Click OK in all dialog boxes.

Calculation:

MINITAB output:

Paired T-Test and CI:Age 14, Age 12

Paired T for Age 14Age12.

NMean        StDev         SE MeanAge 144066.160      2.949          0.466Age 12           40         60.792     3.097          0.490Difference       40         5.3675      0.5797         0.0917  

95% CI for mean difference: (5.1821, 5.5529)

T-test of mean difference =0(vs not =0): T-value=58.56,   P-value=0.000

Form the above MINITAB output, the 95% confidence interval for the mean increase in height for boys between the ages of 12 and 14 is (5.182 inches, 5.5529 inches).

(b)

To determine

To explain whether the confidence interval contradict the claim that mean height is 5.5 inches.

(b)

Expert Solution
Check Mark

Answer to Problem 13E

No. tile confidence interval does not contradicts the claims that “the mean increase in height is 5.5 inches” because the confidence interval contain 5.5 inches.

Explanation of Solution

Calculation:

Check whether the confidence interval contradict the given claim or not.

The 95% t-confidence interval for (μ1μ2) is (5.1821,5.5529) which contain the hypothesized value 5.5 inches. That is, the hypothesized value 5.5 inches lies inside the interval (5.1821,5.5529)

No. the confidence interval does not contradicts the claims that “the mean increase in height is 5.5 Inches” because the confidence interval contain 5.5 inches.

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Chapter 10 Solutions

Elementary Statistics (Text Only)

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