Question

Researchers are investigating the distribution of subscribers to a specific streaming service in different populations. In a random sample of 200 people in City C, 34 were found to subscribe, while in City K, a separate random sample of 200 people revealed 54 subscribers. Assuming all conditions for inference are met, determine which of the following represents a 90 percent confidence interval for the difference in population proportions (City C minus City K) of subscribers to the streaming service:

A. (0.17−0.27)±1.65 × √0.17​/200+0.27/200​​
B. (0.17−0.27)±1.96 × √0.17×0.83/400​+0.27×0.73​​/400
C. (0.17−0.27)±1.65 × √0.17×0.83​/400+0.27×0.73​​/400
D. (0.17−0.27)±1.96 × √0.17×0.83​/200+0.27×0.73​​/200

Answer 1

The 90 percent confidence interval for the difference in population proportions can be calculated using the sample proportions, sample sizes, and a z-value corresponding to the desired confidence level.

Step-by-step explanation:

To find the 90 percent confidence interval for the difference in population proportions, we can use the formula:

(p1 - p2) ± z * √((p1 * (1 - p1))/n1 + (p2 * (1 - p2))/n2)

where:

• p1 and p2 are the sample proportions
• z is the z-value corresponding to the desired confidence level
• n1 and n2 are the sample sizes

In this case, p1 = 34/200 = 0.17, p2 = 54/200 = 0.27, z = 1.65, n1 = 200, and n2 = 200.

Substituting these values into the formula, we get:

(0.17 - 0.27) ± 1.65 * √((0.17 * (1 - 0.17))/200 + (0.27 * (1 - 0.27))/200)

Simplifying the expression gives us:

(-0.1) ± 1.65 * √(0.1393/200 + 0.1811/200)

Finally, evaluating the expression gives us the 90 percent confidence interval for the difference in population proportions.

Therefore answer is C. (0.17−0.27)±1.65 × √0.17×0.83​/400+0.27×0.73​​/400.