Question

A researcher wishes to estimate with 90% confidence the population proportion of adults who think Congress is doing a good or excellent job Herestimate must be accurate within 1% of the true proportion (a) No preliminary mate vale. Find the sample size needed b) Find the minimum samplese needed, using a prior study that found that 25% of the respondents said they think Congress is doing a good or excellent job (c) Compare the results from parts (a) and (b) (a) What is the minimum samplese needed assuming that no prior information is available? (Round up to the nearest whole number as needed) th) What is the minimum sample size needed using a prior study that found that 26% of the respondents said they think Congress is doing a good or excellent job? Round up to the nearest whole number as needed) c) How do the results from (a) and (b)compare? OA. Having an estimate of the population proportion has no effect on the minimum samplesneded OB. Having an estimate of the population proportion raises the minimum sample size needed OC. Having an estimate of the population proportion reduces the minimum sample size needed Click to select your answeris)

Answer 1

Solution :

Given that,

margin of error = E = 0.01

Z_$\alpha$/2 = 1.645

(a)

$\hat p$ = 0.5

1 - $\hat p$ = 0.5

sample size = n = (Z_{$\alpha$ / 2} / E)² * $\hat p$ * (1 - $\hat p$ )

= (1.645 / 0.01)² * 0.5 * 0.5

= 6765.06

sample size = n = 6766

(b)

$\hat p$ = 0.26

1 - $\hat p$ = 0.74

sample size = n = (Z_{$\alpha$ / 2} / E)² * $\hat p$ * (1 - $\hat p$ )

= (1.645 / 0.01)² * 0.26 * 0.74

= 5206.4

sample size = n = 5207

(c)

Option C)