Question

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

Answer 1

Answer:

The correct answer is "1668". A further solution is provided below.

Step-by-step explanation:

According to the question,

Estimated proportion,

$\hat{p} = \frac{574}{1007}$

  $=0.57$

Margin of error,

E = 0.02

Level of confidence,

= 90%

= 0.90

Critical value,

$Z_{0.10}=1.65$

Now,

⇒  $0.02=1.65\times \sqrt{\frac{0.57\times 0.43}{n} }$

 $0.0004=2.7225\times \frac{0.2451}{n}$

         $n=\frac{2.7225\times 0.2451}{0.0004}$

             $=1668.21$

or,

         $n \simeq 1668$