Question

Is your favorite TV program often interrupted by advertising? CNBC presented statistics on the average number of programming minutes in a half-hour sitcom. For a random sample of 20 half-hour sitcoms, the mean number of programming minutes was 23.36 and the standard deviation was 1.13. Assume that the population is approximately normal. Estimate with 97% confidence the mean number of programming minutes during a half-hour television sitcom.  (Round to 2 decimal places.)

Complete the following sentence to provide an interpretation of the confidence interval in the context of the problem:

We are 97% confident that the population mean number of programming minutes for all half-hour television sitcoms is between _______ and _________.

Answer 1

Solution :

Given that,

= 23.36

s = 1.13

n = 20

Degrees of freedom = df = n - 1 = 20 - 1 = 19

At 97% confidence level the t is ,

= 1 - 97% = 1 - 0.97 = 0.03

/ 2 = 0.03 / 2 = 0.015

t _/2,df = t_0.015,19 = 2.346

Margin of error = E = t_/2,df * (s /n)

= 2.346 * (1.13 / 20)

= 0.59

The 97% confidence interval estimate of the population mean is,

- E < < + E

23.36 - 0.59 < < 23.36 + 0.59

22.77 < < 23.95

We are 97% confident that the population mean number of programming minutes for all half-hour

television sitcoms is between 22.77 and 23.95 .