Question

A credit card company wanted to estimate the proportion of its customers who pay their credit card minimum balance on time. The company sampled 500 records and constructed a confidence interval for the true proportion of customers who pay their credit card minimum balance on time. The resulting 95 percent confidence interval was (0.765, 0.835). Which of the following is a true statement regarding the value of the point estimate and margin of error of the percentage of customers who pay their credit card minimum balance on time?

a. The point estimate is 0.765 and the margin of error is 0.07.
b. The point estimate is 0.765 and the margin of error is 0.835.
c. The point estimate is 0.80 and the margin of error is 0.035.
d. The point estimate is 0.80 and the margin of error is 0.07.
e. The point estimate could be any number within the interval and the margin of error is 0.035.

Answer 1

Answer: c. The point estimate is 0.80 and the margin of error is 0.035.

Explanation:

Given: The 95 percent confidence interval was (0.765, 0.835).

Confidence interval = Point estimate ± Margin of error.

I.e. Point estimate + Margin of error = 0.835 (i)

Point estimate - Margin of error = 0.765 (ii)

Add (i) and (ii), we get

2 (Point estimate)= 1.60

⇒ Point estimate = 0.80

Put this in (i), we get

0.80+Margin of error = 0.835

⇒ Margin of error = 0.835 -0.80

⇒ Margin of error = 0.035

Hence, the correct statement is:

c. The point estimate is 0.80 and the margin of error is 0.035.