Question

A survey is planned to determine what proportion of high-school students in a metropolitan school system have regularly smoked marijuana. The school administrators would like to estimate the proportion with 95 % confidence and a margin of error of no more than 4%.

• It was reported that 31.03% of high school students in a similar metropolitan area regularly smoke marijuana. If this estimate is used, what sample size would be required? n =
• If the administrators choose not to use the estimate from the similar metropolitan area, what sample size would be required? n =
• If the level of confidence were increased to 99 %, what would happen to the required sample size?
  • A larger sample size would be required.
  • A smaller sample size would be required.
  • The sample size would not be affected.

Note: Don't forget the rounding rule discussed in class for sample sizes!

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin of Error, E = 0.04

The provided estimate of proportion p is, p = 0.3103
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 = 0.3103*(1 - 0.3103)*(1.96/0.04)^2
n = 513.85

Therefore, the sample size needed to satisfy the condition n >= 513.85 and it must be an integer number, we conclude that the minimum required sample size is n = 514
Ans : Sample size, n = 514

The following information is provided,
Significance Level, α = 0.05, Margin of Error, E = 0.04

The provided estimate of proportion p is, p = 0.5
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 = 0.5*(1 - 0.5)*(1.96/0.04)^2
n = 600.25

Therefore, the sample size needed to satisfy the condition n >= 600.25 and it must be an integer number, we conclude that the minimum required sample size is n = 601
Ans : Sample size, n = 601

A larger sample size would be required.