12.155
12.156
12.157 a
LCL = 6.84, UCL = 6.98
b The histogram is bell shaped.
12.158
12.159
12.160
12.161
2
0:H
= 4
2
1:H
> 4
12.162
p:H0
= .90
12.163
LCL = .937, UCL = 1.263
b
2
0:H
= 10.24 (3.22)
2
1:H
< 10.24
12.165 n =
2
2/
B
)p
ˆ
1(p
ˆ
z
−
=
2
02.
)5.1(5.575.2
−
= 4144
12.166
12.167 Number of cars:
:H0
= 125
Amount of time
:H0
= 3.5
:H1
> 3.5
12.168 a
b.
:H0
= 16
:H1
< 16
12.169
12.170
:H0
= 14.35
:H1
> 14.35
12.171
:H0
= 17.62
:H1
> 17.62
12.172
:H0
= 25.97
:H1
12.173
12.174
:H0
= 65.8
:H1
> 65.8
12.175
12.176 a.
b.
c.
d.
Case 12.1
95% confidence interval estimate of mean weekly consumption per student:
Gross revenue $1,827,000
Less 35% university take $1,187,550
Cost to produce cans $487,200
Current profit $484,000
1
2
3
A B C D
t-Estimate: Mean
Cans
1
2
3
A B C
Case 12.1
Mean number of cans/ student / week 1.218
Gross revenue $2,121,000
Less 35% university take $1,378,650
Cost to produce cans $565,600
Net profit $613,050
Current profit $484,000
Estimated Mean
Number of Cans Current
per Student Revenue Cost Profit Profit Net
LCL = 1.218 $1,187,550 $487,200 $500,350 $484,000 $ 16,350
Case 12.2
Estimated Mean
Number of Cans Current
per Student Revenue Cost Profit Profit Net
LCL = 1.218 $1,187,550 $487,200 $500,350 $855,910 $–355,560
Case 12.3
a 95% confidence interval estimate of the mean medical costs for each of the four age categories:
1
2
3
4
A B C
Case 12.1
Mean number of cans/ student / week 1.414
Number of cans sold annually 2,828,000
1
2
A B C D
t-Estimate: Mean
Estimated annual costs for 2016
Estimate of mean Estimate of total (1,000s)
Age category Number (1,000s) LCL UCL LCL UCL
45 to 64 10,094 1,784 1,877 18,007,696 18,946,438
Estimated annual costs for 2021
Estimate of mean Estimate of total (1,000s)
Age category Number (1,000s) LCL UCL LCL UCL
45 to 64 10,054 1,784 1,877 17,936,336 18,871,358
1
2
3
A B C D
t-Estimate: Mean
Age:65-74
1
2
3
A B C D
t-Estimate: Mean
Age:75-84
1
2
3
A B C D
t-Estimate: Mean
Age:85+
Total 17,036 65,577,095 68,919,207
Estimated annual costs for 2026
Estimate of mean Estimate of total (1,000s)
Age category Number (1,000s) LCL UCL LCL UCL
45 to 64 9,892 1,784 1,877 17,647,238 18,567,284
Estimated annual costs for 2031
Estimate of mean Estimate of total (1,000s)
Age category Number (1,000s) LCL UCL LCL UCL
45 to 64 9,823 1,784 1,877 17,524,232 18,437,771
Estimated annual costs for 2036
Estimate of mean Estimate of total (1,000s)
Age category Number (1,000s) LCL UCL LCL UCL
45 to 64 10,150 1,784 1,877 18,107,600 19,051,550
Case 12.4
a 95% confidence interval estimate of the proportion of Americans with Alzheimer’s disease for each of the three
age categories:
Estimated number of Americans with Alzheimer’s disease for 2015
Estimate of proportion Estimate of total (1,000s)
Age category Number (1,000s) LCL UCL LCL UCL
65 to 74 26,967 .0009 .0025 24.270 67.418
Estimated number of Americans with Alzheimer’s disease for 2020
Estimate of proportion Estimate of total (1,000s)
Age category Number (1,000s) LCL UCL LCL UCL
65 to 74 32,312 .0009 .0025 29.081 80.780
Total 54,804 200.290 337.459
Estimated number of Americans with Alzheimer’s disease for 2025
Estimate of proportion Estimate of total (1,000s)
Age category Number (1,000s) LCL UCL LCL UCL
65 to 74 36,356 .0009 .0025 32.720 90.890
Case 12.5
a. If there is no middle bias the proportion of bets on 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, and 35 is 12/36, or .3333.
b. H0: p = .3333
n/)p1(p
pp
ˆ
z−
−
=
=
,61.26
731,21/)3333.1(3333.
3333..4184. =
−
−
p-value = P(Z > 26.61) = 0. There is overwhelming
evidence of middle bias.
c. If there is no middle bias the proportion of bets on 17 and 20 is 2/36 = .0556.
d. H0: p = .0556
n/)p1(p
pp
ˆ
z−
−
=