Question

A survey of 2276 adults in a certain large country aged 18 and older conducted by a reputable polling organization found that 409 have donated blood in the past two years. Complete parts​ (a) through​ (c) below.

a) Obtain a point estimate for the population proportion of adults in the country aged 18 and older who have donated blood in the past two years. Modifying Above p with caret equals __ ​(Round to three decimal places as​ needed.)

​(b) Verify that the requirements for constructing a confidence interval about p are satisfied. The sample ▼ cannot be assumed to be can be assumed to be is stated to be is stated to not be a simple random​ sample, the value of ▼ ModifyingAbove p with caret left parenthesis 1 minus ModifyingAbove p with caret right parenthesis Modifying Above p with caret n n ModifyingAbove p with caret n ModifyingAbove p with caret left parenthesis 1 minus ModifyingAbove p with caret right parenthesis is nothing​, which is ▼ less than greater than or equal to ​10, and the ▼ sample proportion sample size population proportion population size ▼ is stated to not be is stated to be cannot be assumed to be can be assumed to be less than or equal to​ 5% of the ▼ population size. sample proportion. population proportion. sample size. ​(Round to three decimal places as​ needed.) ​

(c) Construct and interpret a 90​% confidence interval for the population proportion of adults in the country who have donated blood in the past two years. Select the correct choice below and fill in any answer boxes within your choice. ​(Type integers or decimals rounded to three decimal places as needed. Use ascending​ order.)

A. There is a nothing​% probability the proportion of adults in the country aged 18 and older who have donated blood in the past two years is between nothing and nothing.

B. We are nothing​% confident the proportion of adults in the country aged 18 and older who have donated blood in the past two years is between __ and __.

Answer 1

Given, n = 2276 and X = 409

P^ = 409/2276 = 0.1797

n*P(1-P) = 2276*0.1797(1-0.1797) = 335.5

a)

Point estimate P^ = 0.1797

b)

The sample can be assumed to be is stated to be a simple random​ sample, the value of np(1-p) is ​335.5, which is greater than 10, and the sample size is stated to be can be assumed to be less than 5% of the population size.

c)

90% CI

alpha = 0.1

Zc = 1.645 (Use Z table)

CI = P^ +/- Zc * SQRT(P^*(1-P^)/n)

= 0.1797 +/- 1.645*SQRT(0.1797*(1-0.1797)/2276)

= 0.1797 +/- 0.0132

CI = (0.1665, 0.1929)

We are 90% confident the proportion of adults in the country aged 18 and older who have donated blood in the past two years is between 0.1665 and 0.1929