The number of minutes of commercials shown per hour was determined 12 times at random. The results are 14,13,15,11,17,18,11,14,17,18,15 and 13 minutes of commercials shown per hour. Construct a 98% confidence interval for the mean number of minutes of commercials shown per hour.

a. (12.8173,16.5161)

b. (12.7350,16.5984)

c. (12.7350,16.5161)

d. (12.8173,16.5984)

e. (13.1025,16.2309)

b. (12.7350,16.5984)

Step-by-step explanation:

First, find the average and standard deviation of the sample:

x = 14.6667

s = 2.4618

To make a confidence interval of the population:

(μ ± MoE)

where:

μ = x

MoE = CV * s / √n

MoE is the margin of error, CV is the critical value, and s/√n is the standard error.

Looking in a student's t-table, for a 98% confidence interval, and for 12-1=11 degrees of freedom, CV = 2.718.

So the margin of error is:

MoE = 2.718 * 2.4618 / √12

MoE = 1.9316

The confidence interval is therefore:

(14.6667 ± 1.9316)

(12.7351, 16.5983)