Question

In a large city, we are trying to estimate the percentage of college enrollment among all people of age between 18 and 24. (So our population is people of age between 18 and 24 in this city.) We take a simple random sample of 197 from this population. In this sample, we find that 76 are enrolled in college. Find a 95% confidence interval for the rate of college enrollment in the population. (Only enter the upper limit as your answer and include 2 digits after the decimal point.)

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 76 / 197 = 0.386

1 - = 1 - 0.386 = 0.614

Z/2 = Z0.025 = 1.96

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 (((0.386* 0.614) / 197)

= 0.068

A 95% upper limit confidence interval for population proportion p is ,

+ E

= 0.386 + 0.068 = 0.318

upper limit = 0.32