Question

There are 150 members at the First Baptist Church in Memphis, of which 135 say they pray regularly. There are 200 members at Faith Community Church in Nashville, of which 183 say they pray regularly. We would like to calculate a confidence interval for p₁ - p2, the true difference in the proportion of members at each church that pray regularly. Which of the following conditions are met?

I. There are at least 1500 members at the First Baptist Church in Memphis and at least 2000 members at Faith Community Church in Nashville.

II. The counts of "successes" and "failures" in each sample are all at least 10.

III. Two independent random samples were taken.

a. I only

b. II only

c. III only

d. I and III

e. None of the conditions have been met.

Answer 1

The conditions that need to be met to calculate a confidence interval for the difference in the proportion of members who pray regularly at each church are: there are at least 1500 members at the First Baptist Church in Memphis and at least 2000 members at Faith Community Church in Nashville, the counts of 'successes' and 'failures' in each sample are all at least 10, and two independent random samples were taken.

Step-by-step explanation:

The conditions that are met to calculate a confidence interval for p₁ - p2, the difference in the proportion of members at each church that pray regularly, are:

1. There are at least 1500 members at the First Baptist Church in Memphis and at least 2000 members at Faith Community Church in Nashville. (Condition I)
2. The counts of 'successes' and 'failures' in each sample are all at least 10. (Condition II)
3. Two independent random samples were taken. (Condition III)

Therefore, the correct answer is (d) I and III.