Question

A researcher wishes to​ estimate, with 90​% ​confidence, the population proportion of adults who think Congress is doing a good or excellent job. Her estimate must be accurate within 22​% of the true 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 26​% 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 sample size needed assuming that no prior information is​ available?

please help me find all the answer.

Answer 1

a)

When preliminary estimate for proportion is not available then p = 0.50

Sample size = Z2/2 * p ( 1 - p) / E2

= 1.64492 * 0.5 * 0.5 / 0.222

= 13.97

Sample size = 14 (Rounded up to nearest integer)

b)

Sample size = Z2/2 * p ( 1 - p) / E2

= 1.64492 * 0.26 * ( 1 - 0.26) / 0.222

= 10.76

Sample size = 11 (Rounded up to nearest integer)

c)

Using additional information of proportion from part b) dramatically decrease the sample size.