Quiz: Week 7: MyStatLab Quiz This Question: 3 pts (a) No )Fid te (e) Compare the

Question

Quiz: Week 7: MyStatLab Quiz This Question: 3 pts (a) No )Fid te (e) Compare the results from parts (a) and (b). size needed. mannin sample sze needed, uang a por study that sound tat 36% ofthe respondents said they are confidert with their ourry's banking system. n-(Round up to the nearest whole number as needed.) ) What iste minimum, sample szo needed using 1 pro stdy that found tat 36% of the respondents said tey are confident with her n- Round up to the nearest whole number as needed.) o) How do the results from (a) and (b) compare? O A. Having an estimate of the population proportion has no effect on the minimum sample size needed B. Having an estimate of the population proportion raises the minimum sample size needed. O C. Having an estmate of the population proportion reduces the minimum sample size needed

Explanation / Answer

a) At 90% confidence nterval the critical value is z0.05 = 1.645

Margin of error = 0.03

or, z0.05 * sqrt(p(1 - p)/n) = 0.03

or, 1.645 * sqrt(0.5 * 0.5/n) = 0.03

or, sqrt(n) = 1.645 * sqrt(0.5 * 0.5)/0.03

or, sqrt(n) = 27.42

or, n = 752

b) Margin of error = 0.03

or, z0.05 * sqrt(p(1 - p)/n) = 0.03

or, 1.645 * sqrt(0.36 * (1 - 0.36)/n) = 0.03

or, sqrt(n) = 1.645 * sqrt(0.36 * 0.64)/0.03

or, sqrt(n) = 26.32

or, n = 693

c) Option - C is correct.

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