Linda Barnes has learned from prior studies that one out of five applicants gets

Question

Linda Barnes has learned from prior studies that one out of five applicants gets admitted to top MBA programs in the country. She wishes to construct her own 95% confidence interval for the acceptance rate in top MBA programs. How large a sample should she take if she does not want the acceptance rate of the sample to deviate from that of the population by more than nine percentage points? State your assumptions in computing the required sample size. Use Table 1. (Round intermediate calculations to 4 decimal places and "z-value" to 3 decimal places. Round up your answer to the nearest whole number.)

Linda Barnes has learned from prior studies that one out of five applicants gets admitted to top MBA programs in the country. She wishes to construct her own 95% confidence interval for the acceptance rate in top MBA programs. How large a sample should she take if she does not want the acceptance rate of the sample to deviate from that of the population by more than nine percentage points? State your assumptions in computing the required sample size. Use Table 1. (Round intermediate calculations to 4 decimal places and "z-value" to 3 decimal places. Round up your answer to the nearest whole number.)

Explanation / Answer

Solution:

Population proportion is not given, so we assume P=0.5

For 95%, z = 1.96

Z=1.96( rounded to 2 decimals)

d = 0.05

Sample size = (z2*p*(1-p))/d^2

= (1.96*0.5*0.5)/0.05^2

= 196

The sample size required= 196

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