For this problem, carry at least four digits after the decimal in your calculati

Question

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

What percentage of your campus student body is female? Let p be the proportion of women students on your campus.

(a) If no preliminary study is made to estimate p, how large a sample is needed to be 99% sure that a point estimate p will be within a distance of 0.04 from p? (Round your answer up to the nearest whole number.)
= ? students

(b) A report indicates that approximately 59% of college students are females. Answer part (a) using this estimate for p. (Round your answer up to the nearest whole number.)
= ? students

Explanation / Answer

(a) If no preliminary study is made to estimate p, how large a sample is needed to be 99% sure that a point estimate p will be within a distance of 0.04 from p?

Answer : so the margin of error = 0.04

Margin of error = Critical test statistic * Standard error of proportion

Critical test statistic for 99% confidence interval = 2.575

Standard error of proportion = sqrt [p* (1-p)/N] where p is the estimated proportion. For maximum estimate we will use p = 0.5

0.04 = 2.575 * sqrt [0.5 * 0.5/N]

0.04 = 2.575 * 0.5 * sqrt(1/n)

sqrt(n) = 32.1875

n = 1036/1037

so n should be 1036.

(b) A report indicates that approximately 59% of college students are females. Answer part (a) using this estimate for p.

Here p^ = 0.59

so now standard error of proportion = sqrt (0.59 * 0.41/n)

0.04 = 2.575 * sqrt (0.59 * 0.41/n)

sqrt (n/ 0.59 * 0.41) = 64.375

n = 1002.467

so n could be 1003

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