1. End of Section Problem 8.3
A random sample of 80 items is taken, producing a sample mean of 48. The population standard deviation is 4.89. Construct a 90% confidence interval to estimate the population mean.

Appendix A Statistical Tables

(Round your answers to 2 decimal places.)

( ) ≤ μ ≤ ( )

2. End of Section Problem 8.4
A random sample of size 70 is taken from a population that has a variance of 49. The sample mean is 90.4. What is the point estimate of μ? Construct a 94% confidence interval for μ.
Appendix A Statistical Tables

(Round your answers to 2 decimal places.)

The point estimate of μ is ( )
The 94% confidence interval: ( ) ≤ μ ≤ ( )

3. End of Section Problem 8.13
Suppose the following data are selected randomly from a population of normally distributed values.
40 51 43 48 41 57 54
39 40 48 45 39 46

Construct a 95% confidence interval to estimate the population mean.

Appendix A Statistical Tables

(Round the intermediate values to 2 decimal places. Round your answers to 2 decimal places.)

( )≤ μ ≤ ( )

End of Section Problem 8.15
If a random sample of 41 items produces = 134.4 and s = 23.6, what is the 98% confidence interval for μ? Assume x is normally distributed for the population. What is the point estimate?

Appendix A Statistical Tables

(Round your answer to 1 decimal place.)

( ) ≤ μ ≤ ( )

The point estimate is ( ) .

End of Section Problem 8.25
Use the information about each of the following samples to compute the confidence interval to estimate p.

a. n = 48 and = 0.56; compute a 90% confidence interval.
b. n = 297 and = 0.82; compute a 95% confidence interval.
c. n = 1,144 and = 0.59; compute a 90% confidence interval.
d. n = 96 and = 0.32; compute a 88% confidence interval.

Appendix A Statistical Tables

(Round your answers to 3 decimal places.)

a. ( ) ≤ p ≤ ( )
b. ( )≤ p ≤ ( )
c. ( )≤ p ≤ ( )
d. ( )≤ p ≤ ( )

End of Section Problem 8.26
Use the following sample information to calculate the confidence interval to estimate the population proportion. Let x be the number of items in the sample having the characteristic of interest.

a. n = 116 and x = 57, with 99% confidence
b. n = 800 and x = 479, with 97% confidence
c. n = 240 and x = 106, with 85% confidence
d. n = 60 and x = 21, with 90% confidence
Appendix A Statistical Tables

*(Round your answer to 2 decimal places.)
**(Round your answer to 3 decimal places.)

a. ( )* ≤ p ≤ ( ) *
b. ( )** ≤ p ≤ ( )**
c. ( )** ≤ p ≤ ( )**
d. ( )* ≤ p ≤ ( )*

End of Section Problem 8.27
Suppose a random sample of 76 items has been taken from a population and 31 of the items contain the characteristic of interest.

a. Use this information to calculate a 90% confidence interval to estimate the proportion of the population that has the characteristic of interest.
b. Calculate a 95% confidence interval.
c. Calculate a 99% confidence interval.
d. As the level of confidence changes and the other sample information stays constant, what happens to the confidence interval?
Appendix A Statistical Tables

(Round the intermediate values to 2 decimal places. Round your answers to 2 decimal places.)

a. ( )≤ p ≤ ( )
b. ( )≤ p ≤ ( )
c. ( )≤ p ≤ ( )

End of Section Problem 8.33
According to Runzheimer International, in a survey of relocation administrators 63% of all workers who rejected relocation offers did so for family considerations. Suppose this figure was obtained by using a random sample of the files of 522 workers who had rejected relocation offers. Use this information to construct a 95% confidence interval to estimate the population proportion of workers who reject relocation offers for family considerations.

Appendix A Statistical Tables
(Round your answers to 4 decimal places.)

( ) ≤ p ≤ ( )

End of Section Problem 8.35
For each of the following sample results, construct the requested confidence interval. Assume the data come from normally distributed populations.

a. n = 12, = 28.4, s2 = 45.9; 99% confidence for σ2
b. n = 7, = 4.37, s = 1.29; 95% confidence for σ2
c. n = 20, = 105, s = 31; 90% confidence for σ2
d. n = 17, s2 = 16.49; 80% confidence for σ2
Appendix A Statistical Tables
(Round your answers to 2 decimal places.)

a. ( )≤ σ2 ≤ ( )
b. ( )≤ σ2 ≤ ( )
c. ( )≤ σ2 ≤ ( )
d. ( )≤ σ2 ≤ ( )

End of Section Problem 8.37
The Interstate Conference of Employment Security Agencies says the average workweek in the United States is down to only 35 hours, largely because of a rise in part-time workers. Suppose this figure was obtained from a random sample of 20 workers and that the standard deviation of the sample was 5.7 hours. Assume hours worked per week are normally distributed in the population. Use this sample information to develop a 98% confidence interval for the population variance of the number of hours worked per week for a worker. What is the point estimate?

Appendix A Statistical Tables

(Round your answers to 2 decimal places.)

( )≤ σ2 ≤ ( )

The point estimate is ( ) .

End of Section Problem 8.39
Suppose a random sample of 14 people 30–39 years of age produced the household incomes shown here. Use these data to determine a point estimate for the population variance of household incomes for people 30–39 years of age and construct a 95% confidence interval. Assume household income is normally distributed.
$38,200 44,800
33,500 38,000
42,300 32,400
27,400 41,200
46,600 38,500
40,200 31,600
35,500 36,800

Appendix A Statistical Tables
(Round your answers to 2 decimal places.)

The point estimate is ( ).

( )≤ σ2 ≤ ( )

End of Section Problem 8.40
Determine the sample size necessary to estimate μ for the following information.

a. σ = 36 and E = 5 at 95% confidence
b. σ = 4.13 and E = 1 at 99% confidence
c. Values range from 80 to 500, error is to be within 10, and the confidence level is 90%
d. Values range from 50 to 108, error is to be within 3, and the confidence level is 88%

Appendix A Statistical Tables

a. Sample size = ( )
b. Sample size = ( )
c. Sample size = ( )
d. Sample size = ( )