Question

You may need to use the appropriate appendix table or technology to answer this question.

In the spring of 2017, the Consumer Reports National Research Center conducted a survey of 1,007 adults to learn about their major healthcare concerns. The survey results showed that 581 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. (Round your answer to two decimal places.)

(b)At 90% confidence, what is the margin of error? (Round your answer to four decimal places.)

(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. (Round your answer to four decimal places.)

( )to( )

(d)Develop a 95% confidence interval for this population proportion. (Round your answer to four decimal places.)

( )to( )

Answer 1

a)

point estimate of the population proportion = 581/1007 = 0.58

b)

sample proportion, = 0.58
sample size, n = 1007
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.58 * (1 - 0.58)/1007) = 0.0156

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, Zc = Z(α/2) = 1.64

Margin of Error, ME = zc * SE
ME = 1.64 * 0.0156
ME = 0.0256

c)

CI = (0.58 - 1.64 * 0.0156 , 0.58 + 1.64 * 0.0156)
CI = (0.5544 , 0.6056)

0.5544 to 0.6056

d)

sample proportion, = 0.58
sample size, n = 1007
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.58 * (1 - 0.58)/1007) = 0.0156

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.0156
ME = 0.0306

CI = (0.58 - 1.96 * 0.0156 , 0.58 + 1.96 * 0.0156)
CI = (0.5494 , 0.6106)

0.5494 to 0.6106