Question

Confidence Interval Given. Assume I created a 96% confidence interval for the mean hours studied for a test based on a random sample of 100 students. The lower bound of this interval was 3 and the upper bound was 16. Assume that when I created this interval I knew the population standard deviation. Using this information,

(a) Calculate the width of the interval. (

b) Calculate the margin of error for the interval.

(c) Calculate the center of the interval.

(d) What is the sample mean?

(e) What is the z ∗ (or zα/2) from the t-table (table D) used? (f) Calculate the population standard deviation. [Round to 3 decimal places and use the appropriate table, not the Empirical Rule.]

Answer 1

(A)

The width of confidence interval is

Width = 16 - 3 = 13

(B)

The margin of error is half of width of confidence interval. So

ME = Width / 2 = 13 / 2 = 6.5

(C)

The center of interval is

Upper limit -ME = 16 - 6.5 = 9.5

(D)

The sample mean is the center of the interval. So

(e)

Here we have

So from z table, we need to find the z-score that has 0.02 area to its right and 0.98 area to its left. So,

(f)

The population standard deviation is