Interval Estimation
Chapter 8
Interval Estimation
Solutions:
5.a.
b.
c.34.80 1.4 or (33.40 to 36.20)
6.a. 369
b.s = 50
c.369 1.96 (50/)
369 6.20 (362.8 to 375.2)
7.
3.37 1.96
3.37 .05(3.32 to 3.42)
8.a.
12,000 1.645
12,000 231 (11,769 to 12,231)
b.12,000 1.96
12,000 275(11,725 to 12,275)
c.12,000 2.576
12,000 362 (11,638 to 12,362)
d.Interval width must increase since we want to make a statement about with greater confidence.
9.a.Using Excel, = $12.41
b.Using Excel, s = 3.64
c. 1.96
12.41 1.96
12.41 0.92(11.49 to 13.33)
10.
7.75 .50(7.25 to 8.25)
11.a.Using Excel we obtained a sample mean of = 6.34 and a sample standard deviation of 2.163. The confidence interval is shown below:
6.34 1.96 (2.163 /)
6.34 .60
The 95% confidence interval estimate is 5.74 to 6.94.
12.a.minutes
b.minutes
Margin of Error = minutes
c.
3.8 .81 (2.99 to 4.61)
13.a..95
b..90
c..01
d..05
e..95
f..85
14.a.1.734
b.-1.321
c.3.365
d.-1.761 and +1.761
e.-2.048 and +2.048
18.a.
b.
c.t.025 = 2.201
t.025
1.58 2.201
1.58 .09(1.49 to 1.67)
19.
t.025
6.53 2.093
6.53 .25(6.28 to 6.78)
20.a.22.4 1.96
22.4 1.25(21.15 to 23.65)
b.With df = 60, t.025 = 2.000
22.4 2
22.4 1.28(21.12 to 23.68)
c.Confidence intervals are essentially the same regardless of whether z or t is used.
21.
t.025 = 2.365
t.025
108 2.365
108 8.08(99.92 to 116.08)
25.a.
b.
26.a. Use 340
b. Use 1358
c. Use 8487
29.a.
b.
30.
31 .a. = 100/400 = 0.25
b.
c.
.25 1.96 (.0217)
.25 .0424(.2076 to .2924)
32.a..70 1.645
.70 .0267(.6733 to .7267)
b..70 1.96
.70 .0318(.6682 to .7318)
33.
34.Use planning value p = .50
35.a. = 562/814 = 0.6904
b.
c.0.6904 0.0267 (0.6637 to 0.7171)
36.a. = 152/346 = .4393
b.
.4393 1.96(.0267)
.4393 .0523 (.3870 to .4916)
37., = 182/650 = .28
.28 1.96
0.28 0.0345 (0.2455 to 0.3145)
38.a.
b.0.26 0.0430 (0.2170 to 0.3030)
c.
39.a. Use 944
b. Use 1631
40.a. = 255/1018 = 0.2505
b.1.96 = 0.0266
41.
Margin of Error = 1.96= 1.96(.0102) = .02
.16 1.96
.16 .02 (.14 to .18)
8 - 1