Question

Health-Care Survey. In the spring of 2017, the Consumer Reports National Research Center conducted a survey of 1007 adults to learn about their major health-care con-cerns. The survey results showed that 574 of the respondents lack confidence they will be able to afford health insurance in the future.

a. What is the point estimate of the population proportion of adults who lack confidence they will be able to afford health insurance in the future.

b. At 90% confidence, what is the margin of error?

c. Develop a 90% confidence interval for the population proportion of adults who lack confidence they will be able to afford health insurance in the future.

d. Develop a 95% confidence interval for this population proportion

Answer 1

Solution:

n = 1007

x = 574

a) Point estimate = x/n = 574/1007 = 0.57

b) Here , c = 90% = 0.90

= 1 - c = 0.10

= 1.645

Now , the margin of error is given by

E = /2 *  

= 1.645 * [0.57 *(1 - 0.57)/1007]

= 0.0257

c)90% confidence interval is

( - E)   ( + E)

(0.57 - 0.0257)   (0.57 + 0.0257)

0.5443 0.5957

d)For 95% confidence,

= 1.96

E = /2 *  

= 1.96 * [0.57 *(1 - 0.57)/1007]

= 0.0320

95% confidence interval is

( - E)   ( + E)

(0.57 - 0.0320)   (0.57 + 0.0320)

0.5380 0.6020