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,

1. (a) Calculate the width of the interval.

2. (b) Calculate the margin of error for the interval.

3. (c) Calculate the center of the interval.

4. (d) What is the sample mean?

5. (e) What is the z∗ (or zα/2) from the t-table (table D) used?

6. (f) Calculate the population standard deviation. [Round to 3 decimal places and use the

   appropriate table, not the Empirical Rule.]

Answer 1

n = 100

Confidence level = 96%

Lower Bound = 3

Upper Bound = 16

a) Width of the interval = Upper Bound -Lower Bound = 16-3 = 13

b) Margin of error, E = Width/2 = 13/2 = 6.5

c) Center of the interval = Lower Bound +E = 3+6.5 = 9.5

d) Sample mean = 9.5

e) As we knew population standard deviation. so we perform a z-test for confidence interval.

At = 1-0.96 = 0.04, two tailed critical value, = ABS(NORM.S.INV(0.04/2)) = 2.0537

f) Population standard deviation =