Chapter 10
10.1 A point estimator is a single value; an interval estimator is a range of values.
10.3
10.4
10.6
10.7 If there are two unbiased estimators of a parameter, the one whose variance is smaller is
relatively efficient.
10.8
10.9 a.
n/zx 2/
= 100
1.645(25/
50
) = 100
n/zx 2/
n/zx 2/
5.82; LCL = 94.18, UCL = 105.82
10.10 a.
n/zx 2/
= 200
1.96(50/
25
) = 200
n/zx 2/
25
n/zx 2/
25
19.60; LCL = 180.40, UCL = 219.60
10.11 a.
n/zx 2/
= 80
1.96(5/
25
) = 80
n/zx 2/
n/zx 2/
1.96; LCL = 78.04, UCL = 81.96
10.12 a.
n/zx 2/
= 500
2.33(12/
50
) = 500
n/zx 2/
50
n/zx 2/
50
3.95; LCL = 496.05, UCL = 503.95
10.13 a.
n/zx 2/
= 500
2.575(15/
25
) = 500
n/zx 2/
25
n/zx 2/
25
7.73; LCL = 492.27, UCL = 507.73
10.14 a.
n/zx 2/
= 10
1.645(5/
) = 10
n/zx 2/
25
n/zx 2/
.82; LCL = 9.18, UCL = 10.82
10.15 a.
n/zx 2/
= 100
1.96(20/
25
) = 100
n/zx 2/
25
n/zx 2/
25
7.84; LCL = 92.16, UCL = 107.84
10.16 a.
n/zx 2/
= 400
2.575(5/
) = 400
n/zx 2/
n/zx 2/
1.29; LCL = 398.71, UCL = 401.29
10.17 Yes, because the expected value of the sample median is equal to the population mean.
10.19 Because the variance of the sample mean is less than the variance of the sample median, the
sample mean is relatively more efficient than the sample median.
b. The 90% confidence interval estimate of the population mean using the sample mean is 500
2.79.
The 90% confidence interval of the population mean using the sample median is wider than that
10.21
n/zx 2/
= 6.89
1.645(2/
9
) = 6.89
n/zx 2/
1.10; LCL = 5.79, UCL = 7.99
10.23
n/zx 2/
= 22.83
1.96(12/
12
) = 22.83
6.79; LCL = 16.04, UCL = 29.62
10.24
nzx /
2/
= 9.85
1.645(8/
20
) = 9.85
n/zx 2/
n/zx 2/
2.94; LCL = 6.91, UCL = 12.79
10.27
n/zx 2/
= 147.33
1.96(40/
15
) = 147.33
20.24; LCL = 127.09, UCL = 167.57
10.28
n/zx 2/
= 13.15
1.645(6/
13
) = 13.15
n/zx 2/
n/zx 2/
2.74; LCL = 10.41, UCL = 15.89
10.31
n/zx 2/
= 1,810.16
1.96(400/
64
) = 1,810.16
n/zx 2/
200
n/zx 2/
98.00; LCL = 1,712.16,
UCL = 1,908.16
10.34
nzx /
2/
= .510
2.575(.1/
250
) = .510
n/zx 2/
n/zx 2/
250
.016; LCL = .494, UCL = .526. We
estimate that the mean growth rate of this type of grass lies between .494 and .526 inch . This type
of estimate is correct 99% of the time.
10.37
n/zx 2/
= 15.00
2.575(2.3/
) = 15.00
.59; LCL = 14.41, UCL = 15.59.
10.38
n/zx 2/
= 585,063
1.645(30,000/
80
) = 585,063
n/zx 2/
n/zx 2/
5,518; LCL = 579,545,
UCL = 590,581. We estimate that the mean annual income of all company presidents lies between
$579,545 and $590,581. This type of estimate is correct 90% of the time.
10.41 a.
2
2/
B
z
n
=
=
2
10
50645.1
2
2/
B
z
n
=
= 68
10.42 a The sample size increases.
b The sample size increases.
10.43 a.
2
2/
B
z
n
=
=
2
50
250575.2
2
10
250575.2
= 166
2
2/
B
z
n
=
10.44 a The sample size decreases.
b The sample size decreases.
c The sample size increases.
10.47 a. The width of the confidence interval estimate is equal to what was specified.
b. The width of the confidence interval estimate is smaller than what was specified.
b. 500
10
10.49 a.
5500
1537
100
96.1500
n
zx 2/ ==
10.51
2
2/
B
z
n
=
=
2
2
10645.1
= 68
10.52
2
2/
B
z
n
=
=
2
20
360575.2
= 2,149