9.1
25
542/3611=0.15
the requirements are satisfied because the sample size is less than 5% of the population and 3611x0.15x(1-0.15)>10.
lower bound:=0.15-0.01=0.14
upper bound=0.15+0.01=0.16
26
496/1153=0.43
the requirements are satisfied because the sample size is less than 5% of the population and 496x0.43x(1-0.43)>10
lower bound=0.43-0.029=0.402
upper bound=0.43+0.029=0.459
27
521/1003=0.519
the requirements are satisfied because the sample size is less than 5% of the population and 521x0.519x(1-0.519)>10
lower bounds=0.519-0.031=0.489
upper bounds=0.519+0.031=0.55
We can be 95% confident that the porportion of adult Americans who believe that televisions are a luxury they could do without is between 0.489 and 0.55
It is possible that a supermajority (more than 60%) of adult Americans believe that television is a luxury they could do without because the confidence interval is just a way of estimation and it’s possible that the true proportion is not within the interval. However, it is not that likely that the true proportion is greater than 60%.
1-0.489=0.511
1-0.55=0.45
so the 95% confidence interval for the population proportion of adult Americans who believe that televisions are a necessity is (0.45 , 0.511)
28
768/1024=0.75
the requirements are satisfied because the sample size is less than 5% of the population and 768x0.75x(1-0.75)>10
lower bound=0.75-0.035=0.715
upper bound=0.75+0.035=0.785
it is possible that the proportion of adult Americans aged 18 or older for which the issue of family values is extremely or very important in determining their vote for president is below 70%, because the confidence interval is just a way of estimation and it’s possible that the true proportion is not within the interval. However it is not likely because we can be 99% confident that the proportion of adult Americans aged 18 or older for which the issue of family values is extremely or very important in determining their vote for president is between 0.715 and 0.785.
1-0.715=0.285
1-0.785=0.215
so the 99% confidence interval for the proportion of adult Americans aged 18 or older for which the issue of family values is not extremely or very important in determining their vote for president is (0.215 , 0.285).
29
944/1748=0.54
the requirements are satisfied because the sample size is less than 5% of the population and 944x0.54x(1-0.54)>10
lower bound=0.54-0.02=0.52
upper bound=0.54+0.02=0.56
so the 90% confidence interval for the proportion of adult Americans without tattoos who believe individuals with tattoos are more rebellious is (0.52 , 0.56)
upper bound=0.54+0.031=0.571
sp the 99% confidence interval for the proportion of adult Americans without tattoos who believe individuals with tattoos are more rebellious is (0.509 , 0.571)