Question

People were surveyed​ worldwide, being asked the question​ "How important is acquiring wealth to​ you?" Of 1545 respondents in country​ A, 1129 said that it was of more than average importance. In country​ B, of 1323 ​respondents, 594 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.

Answer 1

Answer(a):

For Country A,

We have,

Total number of respondent = n = 1545

Number of respondents who said that acquiring wealth was of more than average importance=x= 1129

The sample proportion is

p= 1129/1545

p= 1129/1545

p= 0.7307443 ≈ 0.731

For Country B,

We have,

Total number of respondent = n = 1323

Number of respondents who said that acquiring wealth was of more than average importance=x= 594

The sample proportion is

p= 594/1323

p= 594/1323

p= 0.4489796 ≈ 0.449

Answer(b):

The necessary condition to be fulfilled is np≥10 and n(1-p)≥10

For country A,

np≥10

1545*0.731= 1129

And

n(1-p)≥10

1545*(1-0.731)=416

Hence both conditions are fulfilled for country A.

Here we have to find 90% confidence interval, that means we have α=0.10

We will require table value of z at α/2

i.e. z(α/2) = z (0.05) = 1.645

The 90% confidence interval of population proportion can be obtained as below:

Lower bound = 0.712

Upper bound = 0.749

For country B,

np≥10

1323*0.449= 594

And

n(1-p)≥10

1323*(1-0.449)=729

Hence both conditions are fulfilled for country B.

Here we have to find 90% confidence interval, that means we have α=0.10

We will require table value of z at α/2

i.e. z(α/2) = z (0.05) = 1.645

The 90% confidence interval of population proportion can be obtained as below:

Lower bound = 0.426

Upper bound = 0.471

The 90% confidence interval of proportion for country A is between 0.712 and 0.749 while the 90% confidence interval of proportion for country B is between 0.426 and 0.471 which indicates that for people of country A the proportion of people who considers that acquiring wealth was of more than average importance is significantly higher than the people of country B.