A nurse in a large university (30,000) is concerned about students eye health. S

Question

A nurse in a large university (30,000) is concerned about students eye health. She taken a random sample of 75 students who don’t wear glasses and finds 27 that need glasses. A. The nurse wants to be able to estimate, with a 95% confidence interval and a margin of error of 6%, the proportion of students who need to wear glasses but don’t. Find the necessary sample size (n) for this estimate. B. The following school year, the nurse wants to construct the same 95% confidence interval for the proportion of students who need glasses but don’t wear them, but she thinks the proportion has changed since last year. Without using the point estimate of the population proportion from the previous year, find the necessary sample size (n) for a 95% confidence interval for the population proportion with a margin of error (m) of 6% A nurse in a large university (30,000) is concerned about students eye health. She taken a random sample of 75 students who don’t wear glasses and finds 27 that need glasses. A. The nurse wants to be able to estimate, with a 95% confidence interval and a margin of error of 6%, the proportion of students who need to wear glasses but don’t. Find the necessary sample size (n) for this estimate. B. The following school year, the nurse wants to construct the same 95% confidence interval for the proportion of students who need glasses but don’t wear them, but she thinks the proportion has changed since last year. Without using the point estimate of the population proportion from the previous year, find the necessary sample size (n) for a 95% confidence interval for the population proportion with a margin of error (m) of 6% A. The nurse wants to be able to estimate, with a 95% confidence interval and a margin of error of 6%, the proportion of students who need to wear glasses but don’t. Find the necessary sample size (n) for this estimate. B. The following school year, the nurse wants to construct the same 95% confidence interval for the proportion of students who need glasses but don’t wear them, but she thinks the proportion has changed since last year. Without using the point estimate of the population proportion from the previous year, find the necessary sample size (n) for a 95% confidence interval for the population proportion with a margin of error (m) of 6%

Explanation / Answer

Here p cap=27/75=0.36

q cap=0.64

Z alpha for 95% CI level=1.96

Margin of error,E=0.06

Formula for n

n={Z alpha/E}^2 (p cap* q cap)

Putting values

N= {1.96/0.06}^2(0.36*0.64)

=246

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