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.)

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MrSmoot MrSmoot · Answer 1 · 2019-04-23T20:58:27+02:00

Answer:

a: 1037 is the minimum sample size needed

b: 712 is the minimum sample size needed

Step-by-step 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