Question

People were surveyed worldwide, being asked the question "How important is acquiring wealth to you?" of 1500 respondents in country A, 1185 said that it was of more than average importance. In country B, of 1302 respondents, 613 said it was of more than average importance.

1) (Round to three decimal places as needed):
a. The sample proportions for country A are: ___
b. The sample proportions for country B are: ___
2) What is the confidence interval for country A? Select the correct choice below and, if necessary, fill in the answer boxes within your choice.
a. The 90% confidence interval for country A is (__%, ___%) [Round to one decimal place as needed.]
b. The conditions for constructing a confidence interval are not satisfied.
3) Compare to the confidence interval for country B. Choose the correct answer below.
a. It is not possible to make a comparaison because the conditions for creating a confidence interval are not satisfied.
b. It appears that the proportion of adults who feel this way in country A is more than those in country B.
c. It appears that the proportion of adults who feel this way in country A is about the same as those in country B.
d. it appears that the proportion of adults who feel this way in country B is more than those in country A.

Answer 1

1) A = 0.79

B = 0.4708

2) CI = (0.7728, 0.8072)

3) CI = (0.4481, 0.4935)

b. It appears that the proportion of adults who feel this way in country A is more than those in country B.

Explanation:

1) Sample proportions for both Population A and B

For country A:

Sample size,n = 1500

Sample proportion =
`(1185)/(1500) = 0.79`

For Country B:

Sample size,n = 1302

Sample proportion =
`(613)/(1302) = 0.4708`

2) Confidence interval for country A:

Given:

Mean,x = 1185

Sample size = 1500

Sample proportion, p = 0.79

q = 1 - 0.79 = 0.21

Using z table,

90% confidence interval,
`Z _\alpha /2 = 1.64`

Confidence interval, CI:

`(p +/- Z_\alpha_/2)/(√((p * q)/n))`

`= (0.79 - 1.64)/(√((0.79 * 0.21)/1500)), (0.79 + 1.64)/(√((0.79 * 0.21)/1500))`

`CI = (0.7728, 0.8072)`

3) Confidence interval for country A:

Given:

Mean,x = 613

Sample size = 1302

Sample proportion, p = 0.4708

q = 1 - 0.4708 = 0.5292

Using z table,

90% confidence interval,
`Z _\alpha /2 = 1.64`

Confidence interval, CI:

`(p +/- Z_\alpha_/2)/(√((p * q)/n))`

`= (0.4708 - 1.64)/(√((0.4708 * 0.5292)/1302)), (0.4708 + 1.64)/(√((0.4708 * 0.5295)/1302))`

`CI = (0.4481, 0.4935)`

From both confidence interval, we could see that that the proportion of adults who feel this way in country A is more than those in country B.

Option B is correct.