Question

In a recent survey of 100 college students, 49% had received the HPV vaccine. Construct a 99% confidence interval for the proportion of college students who have received the vaccine.

- Report the interval as a complete sentence in the context of the problem.

- Would a 95% confidence interval be narrower or wider? Why?

- Is it possible that the true proportion of vaccinate college students is over 50%? Why or why not?

Answer 1

99% confidence interval for p is

- Z/2 * sqrt [ ( 1 - ) / n ] < p < + Z/2 * sqrt [ ( 1 - ) / n ]

0.49 - 2.576 * sqrt [ 0.49 ( 1 - 0.49) / 100 ] < p < 0.49 + 2.576 * sqrt [ 0.49 ( 1 - 0.49) / 100 ]

0.361 < p < 0.619

99% CI is ( 0.361 , 0.619 )

For lower confidence level 95%,

The confidence interval for 95% confidence will be narrower

Since 0.50 contained in confidence interval and some values in the confidence interval are

less than 0.50, it is not possible that the true proportion of vaccinate college students is over 50%.