25.
0.181, or 18.1%.
np-hat(1-p-hat) is greater than or equal to 10 (341.8), and the sample size of 2306 is definitely less than 5% of the population, so the conditions around p are satisfied.
90% C.I = (.168, .194).
90% of the samples will have an interval that contains the value of p, which lies between .168 and .194.
26.
.430 or 43.0%.
np-hat(1-p-hat) is greater than or equal to 10 (282.6), and a sample size of 1153 workers and retirees aged 25 and older is definitely less than 5% of the population, so the conditions around p are satisfied.
95% C.I. = (.401, .459).
95% of all the samples will have an interval that contains the value of p, which lies between .401 and .459.
27.
.519, or 51.9%.
np-hat(1-p-hat) is greater than or equal to 10 (250.3), and the sample size of 1003 adult Americans is definitely less than 5% of the population, so the conditions around p are satisfied.
95% C.I = (.488, .550). 95% of the samples will have an interval that contains the value of p, which lies between .488 and .550.
This is not likely since, the 99% confidence interval states that the highest bound of p is .560.
95% C.I. = (.450, .512).
28.
.750, or 75.0%.
np-hat(1-p-hat) is greater than or equal to 10 (192), and the sample size of 1024 Americans aged 18 or older is definitely less than 5% of the population.
99% C.I = (.715, .785).
Yes this is likely.
99% C.I = (.215, .285).
29.
95% C.I = (.071, .151).
99% C.I = (.058, .164).
Increasing the level of confidence increases the margin of error.