Question

A researcher wishes to​ estimate, with 99​% confidence, the population proportion of adults who think the president of their country can control the price of gasoline. Her estimate must be accurate within 5​% of the true proportion.

a) What is the minimum sample size needed assuming that no prior information is​ available? (round to nearest whole #)

b) What is the minimum sample size needed using a prior study that found that 32​% of the respondents said they think their president can control the price of​ gasoline? (round to nearest whole #)

c) How do the results from ​(a) and ​(b)​ compare?

-Having an estimate of the population proportion has no effect on the minimum sample size needed.

-Having an estimate of the population proportion raises the minimum sample size needed

-Having an estimate of the population proportion reduces the minimum sample size needed

Answer 1

Using z distribution table, z critical value corresponding to 99% confidence interval is 2.58

(A) No prior estimation is given

margin of error = 5% = 5/100 = 0.05

Formula for sample size

Rounding to nearest whole number, we get sample size n = 666

(B) proportion = 32% = 32/100 = 0.32

margin of error = 5% = 5/100 = 0.05

Formula for sample size

Rounding to nearest whole number, we get sample size n = 579

(C) It is clear that the sample size is reduced when we have prior estimation of proportion, i.e. 579.

Therefore, we can say that sample size needed is more for no prior estimation calculation

option C is correct.