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 23 half-hour sitcoms, the mean number of programming minutes was 21.52 and the standard deviation was 1.15. Assume that the population is approximately normal. Estimate with 93% 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 93% confident that the population mean number of programming minutes for all half-hour television sitcoms is between    and .

Answer 1

Solution :

Given that,

= 21.52

s = 1.15

n = 23

Degrees of freedom = df = n - 1 = 23 - 1 = 22

At 93% confidence level the t is ,

= 1 - 93% = 1 - 0.93 = 0.07

/ 2 = 0.07 / 2 = 0.035

t _/2,df = t_0.035,22 = 1.905

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

= 1.905 * (1.15 / 23)

= 0.46

The 93% confidence interval estimate of the population mean is,

- E < < + E

21.52 - 0.46< < 21.52 + 0.46

21.06 < < 21.98

We are 93% confident that the population mean number of programming minutes for all half-hour television sitcoms is between 221.06 and 21.98