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 1​% 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 40​% of the respondents said they think Congress is doing a good or excellent job. ​(c) Compare the results from parts​ (a) and​ (b).

Answer 1

Given data

Error = 1% = 0.01

Confidence level = 0.90

Significance level

Since, population proportion is not given

a)

Assuming

Population proportion = 0.5

Margin of error formula is given by

Simplifying the above formula

b)

Population proportion = 0.4

c)

Sample size is more when preliminary proportion is not given.