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

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

Explanation:

According to the question,

Estimated proportion,

`\hat{p} = (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* \sqrt{(0.57* 0.43)/(n) }`

`0.0004=2.7225* (0.2451)/(n)`

`n=(2.7225* 0.2451)/(0.0004)`

`=1668.21`

or,

`n \simeq 1668`