Question

A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of

25

adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond​ yes, is approximately​ normal, how many more adult Americans does the researcher need to sample in the following​ cases?​(a)

20​%

of all adult Americans support the changes​(b)

25​%

of all adult Americans support the changes

​(a) The researcher must ask

...........????? more American adults. ​(Round up to the nearest​ integer.)​

(b) The researcher must ask

.........???? .American ( Round up to the nearest​ integer.) Two parts must be awnsered thanks

Answer 1

solution:-

formula

=> np should ≥ 10

finding that np(1-p) = 10

(a) here given that p = 0.20

=> np(1-p) = 10

=> n(0.20)*(1-0.20) = 10

=> n(0.20)*(0.80) = 10

=> n(0.16) = 10

=> n = 10/0.16

=> n = 62.5

=> n = 63

from the above question already have 25

=> 63-25 = 38

the researchers must ask 38 more americans

(b) here given that p = 0.25

=> np(1-p) = 10

=> n(0.25)*(1-0.25) = 10

=> n(0.25)*(0.75) = 10

=> n(0.1875) = 10

=> n = 10/0.1875

=> n = 53

from the above question already have 25

=> 53-25 = 28

the researchers must ask 28 more americans