For each set of sample outcomes below, use Formula 6.2 to construct the 95% confidence interval for estimating μ , the population mean. a. X ¯ = 5.2 s = 0.7 N = 157 b. X ¯ = 100 s = 9 N = 620 c. X ¯ = 20 s = 3 N = 220 d. X ¯ = 1020 s = 50 N = 329 e. X ¯ = 7.3 s = 1.2 N = 105 f. X ¯ = 33 s = 6 N = 220

Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

Solutions

Chapter
Section
Chapter 6, Problem 6.1P
Textbook Problem
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For each set of sample outcomes below, use Formula 6.2 to construct the 95% confidence interval for estimating μ , the population mean. a. X ¯ = 5.2 s = 0.7 N = 157 b. X ¯ = 100 s = 9 N = 620 c. X ¯ = 20 s = 3 N = 220 d. X ¯ = 1020 s = 50 N = 329 e. X ¯ = 7.3 s = 1.2 N = 105 f. X ¯ = 33 s = 6 N = 220

Expert Solution
To determine

a.

The 95% confidence interval for estimating the population mean.

Solution:

The 95% confidence interval for estimating μ is 5.2±0.11.

Explanation of Solution

Given Information:

X¯=5.2s=0.7N=157

Formula used:

Confidence interval for a sample mean (large sample, population standard deviation unknown) is given by,

c.i.=X¯±Z(sN1)

Calculation:

The value of statistic at 95% level of significance is given as,

Z0.5=1.96

Substitute 5.2 for X¯, 1.96 for Z, 0.7 for s and 157 for N in the above mentioned formula,

c.i.=X¯±Z(sN1)=5.2±Z(0.71571)=5.2±1.96(0.712.49)=5.2±0.11

Conclusion:

Thus, the 95% confidence interval is 5.2±0.11 for estimating population mean μ.

Expert Solution
To determine

b.

The 95% confidence interval for estimating the population mean.

Solution:

The 95% confidence interval for estimating μ is 100±0.71.

Explanation of Solution

Given Information:

X¯=100s=9N=620

Formula used:

Confidence interval for a sample mean (large sample, population standard deviation unknown) is given by,

c.i.=X¯±Z(sN1)

Calculation:

The value of statistic at 95% level of significance is given as,

Z0.5=1.96

Substitute 100 for X¯, 1.96 for Z, 9 for s and 620 for N in the above mentioned formula,

c.i.=X¯±Z(sN1)=100±Z(96201)=100±1.96(924.87)=100±0.71

Conclusion:

Thus, the 95% confidence interval is 100±0.71 for estimating population mean μ.

Expert Solution
To determine

c.

The 95% confidence interval for estimating the population mean.

Solution:

The 95% confidence interval for estimating μ is 20±0.40.

Explanation of Solution

Given Information:

X¯=20s=3N=220

Formula used:

Confidence interval for a sample mean (large sample, population standard deviation unknown) is given by,

c.i.=X¯±Z(sN1)

Calculation:

The value of statistic at 95% level of significance is given as,

Z0.5=1.96

Substitute 20 for X¯, 1.96 for Z, 3 for s and 220 for N in the above mentioned formula,

c.i.=X¯±Z(sN1)=20±Z(32201)=20±1.96(314.80)=20±0.40

Conclusion:

Thus, the 95% confidence interval is 20±0.40 for estimating population mean μ.

Expert Solution
To determine

d.

The 95% confidence interval for estimating the population mean.

Solution:

The 95% confidence interval for estimating μ is 1020±5.41.

Explanation of Solution

Given Information:

X¯=1020s=50N=329

Formula used:

Confidence interval for a sample mean (large sample, population standard deviation unknown) is given by,

c.i.=X¯±Z(sN1)

Calculation:

The value of statistic at 95% level of significance is given as,

Z0.5=1.96

Substitute 1020 for X¯, 1.96 for Z, 50 for s and 329 for N in the above mentioned formula,

c.i.=X¯±Z(sN1)=1020±Z(503291)=1020±1.96(0.718.11)=1020±5.41

Conclusion:

Thus, the 95% confidence interval is 1020±5.41 for estimating population mean μ.

Expert Solution
To determine

e.

The 95% confidence interval for estimating the population mean.

Solution:

The 95% confidence interval for estimating μ is 7.3±0.23.

Explanation of Solution

Given Information:

X¯=7.3s=1.2N=105

Formula used:

Confidence interval for a sample mean (large sample, population standard deviation unknown) is given by,

c.i.=X¯±Z(sN1)

Calculation:

The value of statistic at 95% level of significance is given as,

Z0.5=1.96

Substitute 7.3 for X¯, 1.96 for Z, 1.2 for s and 105 for N in the above mentioned formula,

c.i.=X¯±Z(sN1)=7.3±Z(1.21051)=7.3±1.96(1.210.20)=7.3±0.23

Conclusion:

Thus, the 95% confidence interval is 7.3±0.23 for estimating population mean μ.

Expert Solution
To determine

f.

The 95% confidence interval for estimating the population mean.

Solution:

The 95% confidence interval for estimating μ is 33±0.79.

Explanation of Solution

Given Information:

X¯=33s=6N=220

Formula used:

Confidence interval for a sample mean (large sample, population standard deviation unknown) is given by,

c.i.=X¯±Z(sN1)

Calculation:

The value of statistic at 95% level of significance is given as,

Z0.5=1.96

Substitute 33 for X¯, 1.96 for Z, 6 for s and 220 for N in the above mentioned formula,

c.i.=X¯±Z(sN1)=33±Z(62201)=33±1.96(614.80)=33±0.79

Conclusion:

Thus, the 95% confidence interval is 33±0.79 for estimating population mean μ.

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