Question

During a blood-donor program conducted during finals week for college students, a blood-pressure reading is taken first, revealing that out of 350 donors, 41 have hypertension. All answers to three places after the decimal. A 95% confidence interval for the true proportion of college students with hypertension during finals week is (WebAssign will check your answer for the correct number of significant figures. , WebAssign will check your answer for the correct number of significant figures. ). We can be 80% confident that the true proportion of college students with hypertension during finals week is WebAssign will check your answer for the correct number of significant figures. with a margin of error of WebAssign will check your answer for the correct number of significant figures. Unless our sample is among the most unusual 10% of samples, the true proportion of college students with hypertension during finals week is between WebAssign will check your answer for the correct number of significant figures. and WebAssign will check your answer for the correct number of significant figures. The probability, at 60% confidence, that a given college donor will have hypertension during finals week is WebAssign will check your answer for the correct number of significant figures. , with a margin of error of WebAssign will check your answer for the correct number of significant figures. Assuming our sample of donors is among the most typical half of such samples, the true proportion of college students with hypertension during finals week is between WebAssign will check your answer for the correct number of significant figures. and WebAssign will check your answer for the correct number of significant figures. We are 99% confident that the true proportion of college students with hypertension during finals week is WebAssign will check your answer for the correct number of significant figures. , with a margin of error of WebAssign will check your answer for the correct number of significant figures. Assuming our sample of donors is among the most typical 99.9% of such samples, the true proportion of college students with hypertension during finals week is between WebAssign will check your answer for the correct number of significant figures. and WebAssign will check your answer for the correct number of significant figures. Covering the worst-case scenario, how many donors must we examine in order to be 95% confident that we have the margin of error as small as 0.01? Using a prior estimate of 15% of college-age students having hypertension, how many donors must we examine in order to be 99% confident that we have the margin of error as small as 0.01?

Answer 1

Sample proportion is

1. 95% confidence interval for population proportion is,

Where,

Therefore 95% confidence interval is,

2.

Margin of error for 80% confidence interval is

We can 80% confident that the true proportion of the college students with hypertension during finals week is 0.117 with margin of error 0.022

3. Among the most unsusal 10% of sample, here we have to compute 90% confidence interval for population proportion,

Where,

Therefore 90% confidence interval is,

4. 99% confidence interval:

Margin of error for 99% confidence interval is

We can 99% confident that the true proportion of the college students with hypertension during finals week is 0.117 with margin of error 0.044