Question

The Behavioral Risk Factor Surveillance System (BRFSS) is an annual telephone survey designed to identify risk factors and report emerging health trends in the population of adults in the U.S. The following table summarizes one variable for the respondents.

Poor	Fair	Good	Very Good	Excellent	Total
677	2019	5675	6972	4657	20000

(a) (1 point) What proportion of the individuals in the survey reported good health? Report the proportion to four decimal places.
(b) (1 point) Suppose that the standard error for the proportion in (a) is 0.0032 and a normal model may reasonably be used. Create a 99% confidence interval for the proportion of U.S. adults who report their health status as good. (Be careful not to mix up percents and proportions in this question.) Recall the general construction of the bounds of the confidence interval follows the formula: point estimate±z∗·SE.
(c) (1 point) Write a sentence that interprets your confidence interval in the context of the data.
(d) (1 point) If you were to construct a 95% confidence interval instead of the 99% CI in (b), determine one thing that would change in your construction.
(e) (1 point) If you were to construct a 95% confidence interval instead of the 99% CI in (b), determine one thing that would stay the same in your construction.

Answer 1

(a)

The proportion of the individuals in the survey reported good health = = 5675/20000 = 0.2838

So,

Answer is:

0.2838

(b)

= 0.2838

=0.01

From Table, critical values of Z = 2.576

Confidence Interval:

= 0.2838 0.008212

= ( 0.2756 ,0.2920)

So,

Answer is:

( 0.2756 ,0.2920)

(c)

he 99% Confidence Interval ( 0.2756 ,0.2920) is a range of values we are 99% confident will contain the unknown population proportion.

(d)

= 0.2838

=0.05

From Table, critical values of Z = 1.96

Confidence Interval:

= 0.2838 0.006249

= ( 0.2776 ,0.2900)

So,

Answer is:

( 0.2776 ,0.2900)

Answer is:

If we were to construct a 95% confidence interval instead of the 99% CI in (b), th one thing that would change in our construction.

critical values of Z

(e)

If we were to construct a 95% confidence interval instead of the 99% CI in (b), th one thing that would stay the same in our construction.

the standard error for the proportion