Question

Use the figure to the right, which shows the percentages of adults from several countries who favor building new nuclear power plants in their country.

The results of the survey in which 1001 adults from Country A, 1025 adults from Country B, 1012 adults from country C, 1018 adults from Country D, and 1010 adults from country E were asked whether national identity is strongly tied to birthplace.

Country a: 36%

County b: 22%

Country c: 28%

Country d: 45%

Country e: 11%

1) The 99% confidence interval for the proportion of adults from Country A who say national identity is strongly tied to birthplace is (__ , __) (Round three decimal places as needed.

2) The 99% confidence interval for the proportion of adults from Country B who say national identity is strongly tied to birthplace is (__ , __) (Round three decimal places as needed.

3) The 99% confidence interval for the proportion of adults from Country C who say national identity is strongly tied to birthplace is (__ , __) (Round three decimal places as needed.

4) The 99% confidence interval for the proportion of adults from Country D who say national identity is strongly tied to birthplace is (__ , __) (Round three decimal places as needed.

5) The 99% confidence interval for the proportion of adults from Country E who say national identity is strongly tied to birthplace is (__ , __) (Round three decimal places as needed.

Answer 1

Solution:

Here, we have to find the confidence intervals for the population proportions. Confidence level for all intervals is given as 99%. The confidence interval formula is given as below:

Confidence interval = P -/+ Z*sqrt(P*(1 – P)/N)

Where, P is the sample proportion, Z is the critical value, and N is the sample size.

C = 99% = 0.99

So, critical value Z = 2.5758 (by using z-table or excel).

Part 1

We are given

P = 0.36, N = 1001, Z = 2.5758

Confidence interval = 0.36 -/+ 2.5758*sqrt(0.36*(1 – 0.36)/1001)

Confidence interval = 0.36 -/+ 2.5758* 0.0152

Confidence interval = 0.36 -/+ 0.0391

Lower limit = 0.36 – 0.0391 = 0.3209

Upper limit = 0.36 + 0.0391 = 0.3991

Confidence interval = (0.3209, 0.3991)

The 99% confidence interval for the proportion of adults from Country A who say national identity is strongly tied to birthplace is (0.321, 0.399).

Part 2

We are given

P = 0.22, N = 1025, Z = 2.5758

Confidence interval = 0.22 -/+ 2.5758*sqrt(0.22*(1 – 0.22)/1025)

Confidence interval = 0.22 -/+ 0.0333

Lower limit = 0.22 – 0.0333 = 0.1867

Upper limit = 0.22 + 0.0333 = 0.2533

The 99% confidence interval for the proportion of adults from Country B who say national identity is strongly tied to birthplace is (0.187, 0.253).

Part 3

We are given

P = 0.28, N = 1012, Z = 2.5758

Confidence interval = 0.28 -/+ 2.5758*sqrt(0.28*(1 – 0.28)/1012)

Confidence interval = 0.28 -/+ 0.0364

Lower limit = 0.28 – 0.0364 = 0.2436

Upper limit = 0.28 + 0.0364 = 0.3164

The 99% confidence interval for the proportion of adults from Country C who say national identity is strongly tied to birthplace is (0.244, 0.316).

Part 4

We are given

P = 0.45, N = 1018, Z = 2.5758

Confidence interval = 0.45 -/+ 2.5758*sqrt(0.45*(1 – 0.45)/1018)

Confidence interval = 0.45 -/+ 0.0402

Lower limit = 0.45 – 0.0402 = 0.4098

Upper limit = 0.45 + 0.0402 = 0.4902

The 99% confidence interval for the proportion of adults from Country D who say national identity is strongly tied to birthplace is (0.410, 490).

Part 5

We are given

P = 0.11, N = 1010, Z = 2.5758

Confidence interval =0.11 -/+ 2.5758*sqrt(0.11*(1 – 0.11)/1010)

Confidence interval =0.11 -/+ 0.0254

Lower limit = 0.11 – 0.0254 = 0.0846

Upper limit = 0.11 + 0.0254 = 0.1354

The 99% confidence interval for the proportion of adults from Country E who say national identity is strongly tied to birthplace is (0.085, 0.135).