Question

In a recent study of 92 eighth graders, the mean number of hours per week that they watched television was 22.6. Assume the population standard deviation is 5.2 hours.

a) Find the 99% confidence interval of the mean.

b) If the standard deviation is doubled to 10.4, what will be the effect on the confidence interval?

Answer 1

a) The 99% confidence interval of the mean is:

[, ], where, = 22.6, = 5.2, n = 92

= [22.6 - 1.3965, 22.6 + 1.3965] = [21.2035, 23.9965] (Ans).

b) If the standard deviation is doubled i.e. = 10.4, then the 99% confidence interval = [22.6 - 2.7931, 22.6 + 2.7931] = [19.8069, 25.3931]. Hence, as the standard deviation is doubled, the margin of error also gets doubled.