Question

A researcher wishes to​ estimate, with 9999​% ​confidence, the population proportion of adults who think Congress is doing a good or excellent job. Her estimate must be accurate within 44​% 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 2222​% 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? nequals=nothing ​(Round up to the nearest whole number as​ needed.)

Answer 1

a: 1037 is the minimum sample size needed

b: 712 is the minimum sample size needed

Explanation:

We need to use the formula for minimum sample size of a proportion when a sample proportion is known.

The level of confidence is 99%, which has a corresponding z-value of 2.575.

We know the desired error is 4%, or 0.04.

Part a: We have no prior estimate. See attached photo for calculation

Part b:

We know p-hat = 0.22. Therefore q-hat = 1 - 0.22 = 0.78

See the attached photo for the calculation of the minimum sample size