Question

Question 24 asks:  In exercise 20B would a sample size of 600 be acceptable? Explain?

20. You wish to estimate with 95% confidence the population proportioln of motor vehicle fatalities taht were caused by alcohol impaired driving. Your estimate must be accurate within 5% of the population proportion. B. Find the minimum sample size needed, using a prior study that found that 31% of motor vehicle fatalities were caused by alcohol impaired driving.

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin of Error, E = 0.05

The provided estimate of proportion p is, p = 0.31
The critical value for significance level, α = 0.05 is 1.96.

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.31*(1 - 0.31)*(1.96/0.05)^2
n = 328.69

Therefore, the sample size needed to satisfy the condition n >= 328.69 and it must be an integer number, we conclude that the minimum required sample size is n = 329
Ans : Sample size, n = 329