A researcher wishes to estimate, with 90% confidence, the population proportion

Question

A researcher wishes to estimate, with 90% confidence, the population proportion of adults who are confident with their country's banking system. His estimate must be accurate within 3% of the population proportion. (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 32% of the respondents said they are confident with their country's banking system. (c) Compare the results from parts (a) and (b). (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

a) when no premilinary estimate is available

then

n = z^2 /(4e^2)

here z = 1.96 for 95 % confidence interval ,

e = 0.03

hence

n = 1.96^2 /(4 * 0.03^2)

= 1067.1111

n = 1068

b) when p^ = 0.32

n = z^2 * p^*q^ /(e^2)

= 1.96^2 * 0.32 *0.68 /0.03^2 = 928.813511

hence n = 929

c) when estimate is not available ,sample size required is more

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