Question

Individual	Television	Radio
1	22	25
2	8	10
3	22	21
4	22	18
5	25	29
6	13	10
7	29	10
8	26	25
9	33	21
10	16	15
11	10	33
12	30	12
13	40	33
14	16	38
15	41	30

In recent years, a growing array of entertainment options competes for consumer time. By 2004, cable television and radio surpassed broadcast television, recorded music, and the daily newspaper to become the two entertainment media with the greatest usage (The Wall Street Journal, January 26, 2004). Researchers used a sample of 15 individuals and collected data on the hours per week spent watching cable television and hours per week spent listening to the radio.

a. Use a .05 level of significance and test for a difference between the population mean usage for cable television and radio. What is the p-value?

b. What is the sample mean number of hours per week spent watching cable television? What is the sample mean number of hours per week spent listening to radio? Which medium has the greater usage?

Answer 1

a) To test H0: There is no significant difference between the population mean usage for cable television and radio.

Against

H1: There is a significant difference between the population mean usage for cable television and radio.

Given alfa = 0.05 level of significance

using t test p- value is obtained as 0.6681

The above p-value is obtained using R-code in R-studio and is as follows:

> #x(hours spent on TV per week),y(hours spent on radio per week)#
> x=c(22,8,22,22,25,13,29,26,33,16,10,30,40,16,41)
> y=c(25,10,21,18,29,10,10,25,21,15,33,12,33,38,30)
> result=t.test(x,y)
> result

   Welch Two Sample t-test

data: x and y
t = 0.4333, df = 27.878, p-value = 0.6681
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-5.716832 8.783498
sample estimates:
mean of x mean of y
23.53333 22.00000

>

Since, p-value(0.6681) is more than the level of sigificance(0.05) then, H0 is accepted abd concluded that there is no significant difference between the population mean usage for cable television and radio.

b) sample mean number of hours per week spent watching cable television = 23.53333

sample mean number of hours per week spent listening to radio =22

Since, 23.53333>22 then, TV medium has greater usage than Radio but this differrence is tested as insignificant for population data as shown in a)