Question

1. 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.

    Individual     Television          Radio

           1                      22                    25

2                      8                      10

3                      25                    29

4                      22                    19

5                      12                    13

6                      26                    28

7                      22                    23

8                      19                    21

9                      21                    21

10                    23                    23

11                    14                    15

12                    14                    18

13                    14                    17

14                    16                    15

15                    24                    23

1. 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? (You must state H₀and Ha, and compute the test statistic.)
2. Provide a 95% confidence interval estimate of the difference between the population mean usage for cable television and radio.

Answer 1

Result:

1. 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.

Individual	Television	Radio	difference
1	22	25	-3
2	8	10	-2
3	25	29	-4
4	22	19	3
5	12	13	-1
6	26	28	-2
7	22	23	-1
8	19	21	-2
9	21	21	0
10	23	23	0
11	14	15	-1
12	14	18	-4
13	14	17	-3
14	16	15	1
15	24	23	1

1. 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? (You must state H0and Ha, and compute the test statistic.)

Difference d = television - radio

Ho: µd=0 H1: µd ≠ 0

= mean of difference( x1-x2)

Paired t Test
Data
Hypothesized Mean Difference	0
Level of significance	0.05
Intermediate Calculations
Sample Size	15
DBar	-1.2000
Degrees of Freedom	14
SD	1.9712
Standard Error	0.5090
t Test Statistic	-2.3577
Two-Tail Test
Lower Critical Value	-2.1448
Upper Critical Value	2.1448
p-Value	0.0335
Reject the null hypothesis

Test statistic t = -2.3577

P value =0.0335

since p value 0.0335 is < 0.05 level of significance, Ho is rejected.

we conclude that there is a significant difference between the population mean usage for cable television and radio.

1. Provide a 95% confidence interval estimate of the difference between the population mean usage for cable television and radio.

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	1.9712
Sample Mean	-1.2
Sample Size	15
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	0.5090
Degrees of Freedom	14
t Value	2.1448
Interval Half Width	1.0916
Confidence Interval
Interval Lower Limit	-2.2916
Interval Upper Limit	-0.1084

95% confidence interval estimate of the difference = (-2.2916, -0.1084)