In: Statistics and Probability
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.
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.