The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day.The assistant provides the following interval estimate: from 740 to 920 books per day.If the head librarian knows that the population standard deviation is 150 books checked out per day,and she asked her assistant for a 95% confidence interval,approximately how large a sample did her assistant use to determine the interval estimate?
A)125
B)13
C)11
D)4

Question

Quizplus · Accepted Answer

For a 95% confidence interval, the critical value for a two-tailed test is 1.96.

The margin of error (E) can be calculated using the formula:

E = z * (sigma/sqrt(n))

where z is the critical value, sigma is the population standard deviation, and n is the sample size.

The given interval estimate is from 740 to 920 books per day, so the point estimate (x̄) is the average of the upper and lower limits:

x̄ = (740 + 920) / 2 = 830 books per day

The margin of error (E) is half of the width of the interval:

E = (920 - 740) / 2 = 90 books per day

Substituting the values into the formula for E, we get:

90 = 1.96 * (150 / sqrt(n))

Solving for n, we get:

n = (1.96^2 * 150^2) / 90^2 = 10.89

Since the sample size must be a whole number, we round up to the nearest integer to get a sample size of 11. Therefore, the best choice is C) 11.

The Head Librarian at the Library of Congress Has Asked