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Chap 12
12.16 a x
Here,
 t / 2s/ n = 350  2.576(100/ 500 ) = 350  11.52; LCL = 338.48, UCL = 361.52
t0.005 comes from the table on p. 262 in the text, using infinite degrees of freedom as an
approximation. A more accurate value, 2.586, can be obtained directly using TINV(0.01, 499)
 in Excel.
 b x  z  / 2  / n = 350  2.575(100/ 500 ) = 350  11.52; LCL = 338.48, UCL = 361.52
c With n = 500 the student t distribution with 499 degrees of freedom is almost identical to the standard
normal distribution.
12.22 x  t  / 2 s / n = 24,051  2.145(17,386/ 15 ) = 24,051  9,628; LCL = 14,422, UCL = 33,680
12.30 x  t  / 2 s / n = 4.66  2.576(2.37/ 240 ) = 4.66  .39; LCL = 4.27, UCL = 5.05
Total number: LCL = 100 million (4.27) = 427 million, UCL = 100 million (5.05) = 505 million
12.34 x  t  / 2 s / n = 2.67  1.973(2.50/ 188 ) = 2.67  .36; LCL = 2.31, UCL = 3.03
12.88 p̂  z  / 2 p̂(1  p̂) / n = .0975
 1.96
.0975 (1  .0975 ) / 2000 = .0975  .0130; LCL = .0845,
UCL = .1105
Number: LCL = 100 million (.0845) = 8.45 million, UCL = 100 million (.1105) = 11.05 million
12.92 p̂  z  / 2 p̂(1  p̂) / n = .1077
 1.96
.1077 (1  .1077 ) / 325 = .1077  .0337; LCL = .0740,
UCL = .1414; Market segment size: LCL = 35.6 million(.0740) = 2.634 million,
UCL = 35.6 million(.1414) = 5.034 million
Case 12.2
Estimated Mean
Number of Cans
per Student
Current
Revenue
Cost
Profit
LCL = 1.218
$1,187,550
$487,200
$500,350
UCL = 1.414
1,378,650
565,600
613,050
Profit
$855,910
1,071,290
Net
$–355,560
–458,240
Coke would not sign the exclusivity agreement. Coke is expected to lose from the exclusivity agreement
because they currently have a much larger share of the market and would not gain by paying for exclusivity.
73,730,628
Case 12.4
a 95% confidence interval estimate of the mean medical costs for each of the four age categories:
1
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
A
B
t-Estimate: Mean
C
Age:45-64
1808
826
1643
1972
Mean
Standard Deviation
LCL
UCL
A
B
t-Estimate: Mean
C
C
D
Age:75-84
8074
3186
7876
8272
Mean
Standard Deviation
LCL
UCL
A
B
t-Estimate: Mean
D
Age:65-74
4494
1820
4381
4607
Mean
Standard Deviation
LCL
UCL
A
B
t-Estimate: Mean
D
C
D
Age:85+
15957
6207
15572
16342
Mean
Standard Deviation
LCL
UCL
b Estimated annual costs for 2003
Estimate of mean
Age category Number (1,000s)
LCL
UCL
Estimate of total (1,000s)
LCL
UCL
2
45 to 64
7,932
1,784
1,877
14,150,688
14,888,364
65 to 74
2,187
4,381
4,607
9,581,247
10,075,509
75 to 84
1,423
7,876
8,272
11,207,548
11,771,056
7,007,400
7,353,900
41,946,883
44,088,829
85 and over
Total
450
15,572 16,342
11,992
Estimated annual costs for 2006
Estimate of mean
Age category Number (1,000s)
LCL
UCL
Estimate of total (1,000s)
LCL
UCL
45 to 64
8,678
1,784
1,877
15,481,552
16,288,606
65 to 74
2,253
4,381
4,607
9,870,393
10,379,571
75 to 84
1,486
7,876
8,272
11,703,737
12,292,192
8,767,036
9,200,546
45,822,717
48,160,915
85 and over
Total
563
15,572 16,342
12,980
Estimated annual costs for 20011
Estimate of mean
Age category Number (1,000s)
LCL
UCL
Estimate of total (1,000s)
LCL
UCL
45 to 64
9,649
1,784
1,877
17,213,816
18,111,173
65 to 74
2,609
4,381
4,607
11,430,029
12,019,663
75 to 84
1,546
7,876
8,272
12,176,296
12,788,512
10,775,824
11,308,664
51,595,965
54,228,012
85 and over
Total
692
15,572 16,342
14,496
Estimated annual costs for 2016
Estimate of mean
Age category Number (1,000s)
LCL
UCL
Estimate of total (1,000s)
LCL
UCL
45 to 64
9,883
1,784
1,877
17,631,272
18,550,391
65 to 74
3,273
4,381
4,607
14,339,013
15,078,711
75 to 84
1,645
7,876
8,272
12,956,020
13,607,440
12,208,448
12,812,128
57,134,753
60,048,670
85 and over
Total
784
15,572 16,342
15,585
Estimated annual costs for 2021
Estimate of mean
Age category Number (1,000s)
LCL
UCL
Estimate of total (1,000s)
LCL
UCL
3
45 to 64
9,840
1,784
1,877
17,554,560
18,469,680
65 to 74
3,886
4,381
4,607
17,024,566
17,902,802
75 to 84
1,938
7,876
8,272
15,263,688
16,031,136
13,173,912
13,825,332
63,016,726
66,228,950
85 and over
Total
846
15,572 16,342
16,510
Estimated annual costs for 2026
Estimate of mean
Age category Number (1,000s)
LCL
UCL
Estimate of total (1,000s)
LCL
UCL
45 to 64
9,636
1,784
1,877
17,190,624
18,068,772
65 to 74
4,364
4,381
4,607
19,118,684
20,104,948
75 to 84
2,459
7,876
8,272
19,367,084
20,340,848
14,481,960
15,198,060
85 and over
Total
930
17,389
15,572 16,342
70,158,352
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