6.3.19-T Question Help A researcher wishes to estimate, with 95% confidence, the

Question

6.3.19-T Question Help A researcher wishes to estimate, with 95% confidence, the population proportion of adults who are confident with their countr s banking system. His esti must be accurate within 5% of the population (a) No preliminary estimate is available. Find the minimum sample size needed b) Find the minimum sample size needed, using a prior study that found that 28% of the respondents said they are confident with their countr s bankin system (c) Compare the results from parts (a) and (b) on. (a) What is the minimum sample size needed assuming that no prior information is available? n(Round up to the nearest whole number as needed,)

Explanation / Answer

we are given

a)

        Z0.05/2*(p*(1-p)/n)1/2 = 0.05 => 1.96*(p*(1-p)/n)1/2 = 0.05

while for p*(1-p), when p=1/2, p*(1-p) arrive maximum and maximum value is ¼, so n =1537*1/4 =384.25

So if no estimate were available for the proportion that support current policy, we need 384 sample size.

B)

Z0.025*(0.28*0.72/n)1/2 = 0.05 => 1.96*(0.2016/n)1/2 = 0.05

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