Question

A 90% confidence interval for a proportion is found to be (0.52, 0.58). What isthe sample proportion?A. 0.56B. 0.54C. 0.55D. 0.58

Answer 1

Answer: 0.55 (choice C)

Step-by-step explanation:

L = lower bound

U = upper bound

The confidence interval (L, U) is (0.52, 0.58)

Find the midpoint of L and U

(L+U)/2 = (0.52+0.58)/2 = 0.55

The exact middle of the confidence interval is the location of the point estimate, which in this context is the sample proportion.

Extra info: the margin of error is 0.03 since 0.55-L = 0.55-0.52 = 0.03 and also U - 0.55 = 0.58 - 0.55 = 0.03

Answer 2

Sarai, if the confidence interval is (0.52, 0.58), therefore:

0.52 + 0.03 = 0.55

0.58 - 0.03 = 0.55

The sample proportion is C. 0.55

Sarai, the definition of a confidence interval is how much uncertainty there is with any particular statistic. Confidence intervals are often used with a margin of error. In our question, the margin of error is 0.03, that is added and subtracted from the sample proportion to calculate the upper and lower limits of the confidence interval.

Using a confidence level of 90%, we got a margin of error of 0.03

Using a different confidence level, we should get a different margin of error.

The formula of the margin of error is: