In a sample of 100 teenagers, 80 reported that they were in favor of an increase in the minimum wage and 20 were against it because they feared a loss of available jobs.Based on this sample, find the .95 confidence interval for the true proportion in the population of teenagers who would favor an increase in the minimum wage.
A) .70 to .90
B) .72 to .88
C) .76 to .84
D) .78 to .82

Question

Quizplus · Accepted Answer

To find the confidence interval, we use the formula:

p ± z*sqrt(p(1-p)/n)

where p is the sample proportion, z* is the z-score that corresponds to the desired level of confidence (in this case, 1.96 for a 95% confidence interval), and n is the sample size.

In this case, p = 0.8 (80 out of 100 teenagers favor an increase in the minimum wage), z* = 1.96, and n = 100.

Using these values, the confidence interval is:

0.8 ± 1.96*sqrt(0.8*0.2/100)
= 0.8 ± 0.098
= (0.702, 0.898)

So the best choice is B, which represents this confidence interval as .72 to .88 (rounded to two decimal places).

In a Sample of 100 Teenagers, 80 Reported That They