Question

In a certain region, 21% of people over age 50 didn't graduate from high school. we would like to know if this percentage is the same among the 25-30 year age group. use critical values to exactly 3 decimal places. (a) how many 25-30 year old people should be surveyed in order to estimate the proportion of non-grads to within 10% with 95% confidence?

Answer 1

To estimate the proportion of non-graduates in the 25-30 year age group within a margin of error of 10% and a confidence level of 95%, we need to survey 248 people.

Step-by-step explanation:

To estimate the proportion of non-graduates in the 25-30 year age group within a margin of error of 10% and a confidence level of 95%, we can use the formula for sample size:

n = (Z^2 * p * (1-p)) / E^2

Where:
n = sample size
Z = Z-score corresponding to the desired confidence level (1.96 for 95% confidence)
p = estimated proportion of non-graduates among people aged 25-30 (assume it is the same as the proportion for people over 50, 21%)
E = margin of error (10%)

Plugging in the values:

n = (1.96^2 * 0.21 * (1-0.21)) / 0.1^2

n = 247.57

Since we can't have a fraction of a person, we need to round up to the nearest integer. Therefore, we should survey 248 25-30 year old people to estimate the proportion of non-graduates within 10% with 95% confidence.