Question

10.21 How do ratings of TV and phone services compare? File Telecom contains a rating of 13 different providers. a. At the 0.05 level of significance, is there evidence of a difference in the mean service rating between TV and phone services?

b. What assumption is necessary about the population distribution in order to perform this test?

c. Use a graphical method (show distribution, rejection and acceptance regions) to evaluate the validity of the assumption in (a).

d. Construct and interpret a 95% confidence interval estimate of the difference in the mean service rating between TV and phone services.

Provider	TV	Internet
Verizon FIOS	71	71
AT&T U-verse	70	69
Cox Communicaitons	61	62
SuddenLink	63	66
Optimum	66	68
Comcast Xfinity	58	60
TimeWarner	60	62
Mediacom	56	58
Spectrum	63	65
Frontier Communications	60	56

Answer 1

a). hypothesis:-

is the difference between mean ratings of TV services and internet services of a provider.

necessary calculation be:-

TV ()	Internet()
71	71	0	0.81
70	69	1	3.61
61	62	-1	0.01
63	66	-3	4.41
66	68	-2	1.21
58	60	-2	1.21
60	62	-2	1.21
56	58	-2	1.21
63	65	-2	1.21
60	56	4	24.01
		sum =   -9	sum = 38.9

test statistic be:-

degrees of freedom = (n-1) = (10-1) =9

for 95 % confidence level ,df = 9, both tailed test, the critical value of t be:-

[ from t distribution table]

rejection region :-

reject the null hypothesis if,

or

decision:-

here, t = -1.369 > -2.262

so, we fail to reject the null hypothesis.

we conclude that,

at the 0.05 level of significance, there is not enough evidence to claim that there is a difference in the mean service rating between TV and phone services.

b). assumptions:-

we assume that the population follows an normal distribution.

validation:-

the probability plot be:-

it is clear that the data follow a normal distribution.

c).the diagram be:-

d).the 95% confidence interval be:-

= ( -2.387 , 0.587 )

we are 95 % confident that the mean difference of ratings for TV and internet service of a provider will lie within the interval ( -2.387 , 0.587 )

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