25.
p=417/2306=0.181
np(1-p)=2306 x 0.181(1-0.181)=341.84≥10, less than 5% of the population.
LB: 0.181-1.645 x √0.181(1-0.181)/2306=0.168 UB: 0.181+1.645 x √0.181(1-0.181)/2306=0.194
We are 90% confident that the population proportion of adult Americans who have donated blood in the past two years is between 0.168 and 0.194.
26.
p=496/1153=0.43
np=(1-p)=1153 x 0.43(1-0.43)=282.6≥10, less than 5% of the population.
LB: 0.43-1.96 x √0.43(1-0.43)/1153=0.401 UB: 0.43+1.96 x √0.43(1-0.43)/1153=0.459
We are 95% confident that the population proportion of workers and retirees in the United States 25 years of age and older who have less than $10,000 in savings is between 0.401 and 0.459.
27.
p=521/1003=0.519
np(1-p)=1003 x 0.519(1-0.519)=250.39≥10, less than 5% of the population.
LB: 0.519-1.96 x √0.519(1-0.519)/1003=0.488 UB: 0.519+1.96 x √0.519(1-0.519)/1003=0.550 We are 95% confident that the population proportion of adult Americans who believe that televisions are a luxury they could do without is between 0.488 and 0.550.
It is possible that more than 60% believe so because maybe the true proportion is not included in the confidence interval. But it is not likely because 0.6 is not include in the confidence interval, it’s outside of confidence interval.
LB: 1-0.550=0.450 UB: 1-0.488=0.512
28.
p=768/1024=0.75
np(1-p)=1024 x 0.75(1-0.75)=192≥10, less than 5% of the population.
LB: 0.75-2.575 x √0.75(1-0.75)/1024=0.715 UB: 0.75+2.575 x √0.75(1-0.75)/1024=0.785
It is possible that the proportion is below 70% because maybe the true proportion is not included in the confidence interval. But it is not likely because 0.7 is out of the confidence interval.
LB: 1-0.785=0.215 UB: 1-0.715=0.285
29.
p=26/234=0.111 LB: 0.111-1.96 x √0.111(1-0.111)/234=0.071 UB: 0.111+1.96 x √0.111(1-0.111)/234=0.151
LB: 0.111-2.575 x √0.111(1-0.111)/234=0.058 UB: 0.111+2.575 x √0.111(1-0.111)/234=0.164
Increasing the confidence level would increases the margin of error.