Question

Confidence Interval Given. Assume I created a 95% confidence interval for the mean hours studied for a test based on a random sample of 64 students. The lower bound of this interval was 4 and the upper bound was 14. 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) used? (f) Calculate the population standard deviation. [Round to 3 decimal places and use the appropriate table, not the Empirical Rule.]

Answer 1

a)

Width of CI = Upper bound - Lower bound

= 14 - 4

= 10

b)

Margin of error E = Width of CI / 2

= 10 / 2

= 5

c)

Center of interval = (14 + 4) / 2

= 9

d)

Sample mean = Upper bound - E

= 14 - 5

= 9

e)

From Z table ,

At 0.05 significance level = Z/2 = 1.96

f)

Margin of error = Z/2 * / Sqrt (n)

5 = 1.96 * / sqrt ( 64)

Solve for

= 20.408