Question

Suppose that a random sample of 100 part-time college students is 68% female. In this activity, we calculate the 95% confidence interval for the proportion of all part-time college students that are female.  

Recall that the 95% confidence interval is:
sample proportion ± 2(SE) where SE is the standard error (or standard deviation).

question 2: State the confidence interval. Then convert the values to percentages and interpret the confidence interval in context.

Answer 1

a)

SE = sqrt [ ( 1 - ) / n ]

= sqrt [ 0.68 ( 1 - 0.68) / 100 ]

= 0.0466

95% confidence interval for p is

2 * SE

0.68 2 * 0.0466

0.68 - 2 * 0.0466 < p < 0.68 * 2 * 0.0466

0.587 < p < 0.773

b)

Confidence interval is ( 0.587 , 0.773 )

In percentage , CI = (58.7% , 77.3% )

interpretation - We are 95% confident that the population proportion falls between 58.7% and 77.3%