Question

In: Statistics and Probability

People were surveyed​ worldwide, being asked the question​ "How important is acquiring wealth to​ you?" Of...

People were surveyed​ worldwide, being asked the question​ "How important is acquiring wealth to​ you?" Of 1513 respondents in country​ A, 1102 said that it was of more than average importance. In country​ B, of 1294 ​respondents, 611 said it was of more than average importance. ​a) What proportion thought acquiring wealth was of more than average importance in each​ country's sample? ​b) Create a 90 ​% confidence interval for the percentage of people who thought it was of more than average importance in country A.​ (Be sure to test​ conditions.) Compare that to a confidence interval for the country B population. ​a) The sample proportions are nothing for country A and nothing for country B. ​(Round to three decimal places as​ needed.) ​b) 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 left parenthesis nothing % comma nothing % right parenthesis . ​(Round to one decimal place as​ needed.) B. The conditions for constructing a confidence interval are not satisfied. Compare to the confidence interval for country B. Choose the correct answer below.

The sample proportions are

nothing

for country A and

nothing

for country B.

​(Round to three decimal places as​ needed.)

​b) 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

left parenthesis nothing % comma nothing % right parenthesis

.

​(Round to one decimal place as​ needed.)

B.

The conditions for constructing a confidence interval are not satisfied.

Compare to the confidence interval for country B. Choose the correct answer below.

A.

It is not possible to make a comparison 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 about the same as those in country B.

C.

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

Solutions

Expert Solution

a) For country A:

n1 = 1513, x1 = 1102

p̂1 = x1/n1 = 0.728

For country B:

n2 = 1294, x2 = 611

p̂2 = x2/n2 = 0.472

b) A. 90% Confidence interval for country A:  

At α = 0.1, two tailed critical value, z_c = NORM.S.INV(0.1/2) =    1.645

Lower Bound = p̄ - z_c*√( p̄ *(1- p̄ )/n) = 0.7284 - 1.645 *√(0.728*0.272/1513) =    0.710

Upper Bound = p̄ + z_c*√( p̄ *(1- p̄ )/n) = 0.7284 + 1.645 *√(0.728*0.272/1513) =    0.747

71.0% < p < 74.7%

--

B)  90% Confidence interval for country B:  

At α = 0.1, two tailed critical value, z_c = NORM.S.INV(0.1/2) =    1.645

Lower Bound = p̄ - z_c*√( p̄ *(1- p̄ )/n) = 0.4722 - 1.645 *√(0.4722*0.5278/1294) =    0.449

Upper Bound = p̄ + z_c*√( p̄ *(1- p̄ )/n) = 0.4722 + 1.645 *√(0.4722*0.5278/1294) =    0.495

44.9% < p < 49.5%

Answer: C.

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


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