Question

The accompanying table contains the service ratings of 14 different Internet and TV providers. Complete parts​ (a) through​(d) below

At the 0.01 level of​ significance, is there evidence of a difference in the mean service rating between TV and Internet​services?Let mu 1be the mean TV service rating and let mu 2 be the mean Internet service rating. State the null and alternative hypotheses. Choose the correct answer below.

b.Determine the T Test and critical values

c. Determine the P value

d Construct and interpret a 90​% confidence interval estimate of the difference in the mean service rating between TV and Internet services aswell as a 95% confidence interval estimate

Provider          TV       Internet

1          65 69

2 57 59

3 71 75

4          67 71

5 67 69

6          63 66

7          55 56

8          64 66

9          76 77

10        74        77

11 75 77

12 68 73

13        64 67

14 61 65

Answer 1

A)
H0= Both means are equal

H1=Means are not equal

Using a 0.01 level of significance

Two-Sample T-Test and CI: TV, Internet

Two-sample T for TV vs Internet

N Mean StDev SE Mean
TV 14 66.21 6.33 1.7
Internet 14 69.07 6.53 1.7

Difference = μ (TV) - μ (Internet)
Estimate for difference: -2.86
99% CI for difference: (-9.63, 3.92)
T-Test of difference = 0 (vs ≠):

DF = 25

b)

T-Value = -1.18

C)

P-Value = 0.251

Here P value is greater than 0.05 so we accept H0 so there is no difference between this two Tv and internet both means are same.

d)

90​% confidence interval estimate of the difference in the mean service rating between TV and Internet services

=90% CI for difference: (-7.01, 1.29)

95​% confidence interval estimate of the difference in the mean service rating between TV and Internet services

=95% CI for difference: (-7.86, 2.15)