25.
a.) 417/2306 = 0.181. This is the point estimate, p hat.
one needs to be that np(1-p) is greater than or equal to 10. Here we will use p hat as p to calculate; the expression is 2306*0.181 (1-0.181) which is equal to 341.84 which is greater than 10. Another requirement is that the sample (n) is less than or equal to 5% of population (N) and in this case it is.
using the formula, the lower bound is 0.168 and the upper bound is 0.194. CI of 90% = (0.168, 0.194) for those 18 years and older who have donated blood in the ast two years.
We are 90% confident that 90% of the population proportion of adult americans 18 years and older who have donated blood in the past two years is between 0.168 and 0.194.
26.
496/1153 = 0.43 as the point estimate, p hat.
one reqirements needs to be np(1-p) is greater than or equal to 10. Here we will use p hat as p to calcualte. Here is it 1153*0.43= (1-0.43)= 282.6 and that is greater than 10. The other reqirement is that the sample (n) is less than or equal to 5% of the population (N) and in this case it is.
using the formula, the lower bound is 0.403 and the upper bound is 0.457. CI of 95%= (0.403, 0.457) for those adult workers and retirees 25 years and older that have less than $10,000 saved
We are 95% confident that the population proportion of of adult workers and retirees 25 years and older that have less than $10,000 saved is between 0.403 and 0.457.
27.
the point etimate is 521/1003= 0.519, also p hat.
one requirement is that np(1-p) must be greater than or equal to 10. Here we will use p hat as p. 1003*0.519(1-0.519)= 250.39 which is greater than 10. Another requirment is that the sampele size (n) is less than or equal to 5% of the population (N) and in this case it is.
using the formula, the lower bound is 0.488 and the upper bound is 0.550. CI of 95% = (0.488, 0.550) for those adult americans that believe television is a luxuary they can do without.
It is possible that the population proportion is more than 60% because of the possibility that the true proportion was not captured in the confidence interval. It is unlikley because 0.6 is outside of the confidence interval.
the lower bound of the necessity belief is 1 minus the upper bound of the luxary: 1-0.550 = 0.450. the upper bound of the necessity belief is 1 minus the lower bound of the luxary belief: 1-0.488 = 0.512. CI of 95% = (0.450, 0.512)
28.
768/1024 = 0.75 as the point estimate, or p hat.
one requirement is that np (1-p) is greater than or equal to 10 and in this case we are replacing p with p hat. 1024*0.75 (1-0.75)= 192 which is greater than 10. Another requirement is that sample size (n) has to be less than or equal to 5% of the population (N) and in this case it is.
the upper bound is 0.715 and the lower bound is 0.785. the CI for 99% is (0.715, 0.785) for those who find family values extremely important in selecting a canidate.
It is possible because there is a chance that the confidence interval did not capture the true proportion. It is not likley that it is below 70% because the interval is between 0.717 (71.5%) and 0.785 (78.5%) and that is a 70% does no fall within that range at all; it has missed the mark.
The lower bound of those 18 or older who do not use family values as a consideration for their canidate vote is 1 minus the upper bound of those who do: 1-0.785 = 0.215. The upper bound of those 18 or older who do not use family values as a consideration for thier candiate vote is 1 minus the lower bound of those who do: 1-0.715= 0.285.
29.
The 95% CI for proportion of men treated with the gel who will expereince elevated PSA levels is (0.071, 0.15)
The 99% CI for proportion of men treated with gel who will experience elevated PSA levels is (0.059, 0.162)
Increasing the conidence level will increase the z score value which means that your lenght of interval will increase as well which means that your margin of error is ultimatley increased as well becuase it is such a large range that the values start to lose significance because it is so broad.