For each set of sample outcomes below, use Formula 6.2 to construct the 95% confidence interval for estimating
a. 

b. 

c. 

d. 

e. 

f. 

a.
The 95% confidence interval for estimating the population mean.
Solution:
The 95% confidence interval for estimating
Given Information:
Formula used:
Confidence interval for a sample mean (large sample, population standard deviation unknown) is given by,
Calculation:
The value of statistic at 95% level of significance is given as,
Substitute
Conclusion:
Thus, the 95% confidence interval is
b.
The 95% confidence interval for estimating the population mean.
Solution:
The 95% confidence interval for estimating
Given Information:
Formula used:
Confidence interval for a sample mean (large sample, population standard deviation unknown) is given by,
Calculation:
The value of statistic at 95% level of significance is given as,
Substitute 100 for
Conclusion:
Thus, the 95% confidence interval is
c.
The 95% confidence interval for estimating the population mean.
Solution:
The 95% confidence interval for estimating
Given Information:
Formula used:
Confidence interval for a sample mean (large sample, population standard deviation unknown) is given by,
Calculation:
The value of statistic at 95% level of significance is given as,
Substitute 20 for
Conclusion:
Thus, the 95% confidence interval is
d.
The 95% confidence interval for estimating the population mean.
Solution:
The 95% confidence interval for estimating
Given Information:
Formula used:
Confidence interval for a sample mean (large sample, population standard deviation unknown) is given by,
Calculation:
The value of statistic at 95% level of significance is given as,
Substitute 1020 for
Conclusion:
Thus, the 95% confidence interval is
e.
The 95% confidence interval for estimating the population mean.
Solution:
The 95% confidence interval for estimating
Given Information:
Formula used:
Confidence interval for a sample mean (large sample, population standard deviation unknown) is given by,
Calculation:
The value of statistic at 95% level of significance is given as,
Substitute
Conclusion:
Thus, the 95% confidence interval is
f.
The 95% confidence interval for estimating the population mean.
Solution:
The 95% confidence interval for estimating
Given Information:
Formula used:
Confidence interval for a sample mean (large sample, population standard deviation unknown) is given by,
Calculation:
The value of statistic at 95% level of significance is given as,
Substitute 33 for
Conclusion:
Thus, the 95% confidence interval is
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