1021 How do the ratings of TV and phone services compare TV

10.21 How do the ratings of TV and phone services compare? TV Provider Phone ROW The file Telecom contains the rating of 13 different providers. 78 Verizon FIOS 74 (Data extracted from \"Ratings: TV, Phone, and Internet Services,\" Consumer Reports, May 2012, p. 25. 83 WOW 74 a. Al the 0.05 level of significance, is there evidence of a difference 70 77 3 Bright House Networks in the mean service rating between TV and phone services? b. What assumption is necessary about the population distribution 68 72 AT&T; U-verse in order to perform this test? Cox 67 74 c. Use a graphical method to evaluate the validity of the assump- Sudden Link 66 tion in (a). 81 d. Construct and interpret a 95% confidence interval estimate 64 75 Cablevision/Optimum of the difference in the mean service rating between TV and 64 73 phone services. Insight 62 RCN 71 70 10 Comcast 61 60 11 Time Warner 71 59 Charter 12 71 54 63 Mediacom 13 KE: will De adoing iu.LI Page 300 Jack, It looks like you did the wrong test. Each part is worth 6 points. Part a Ho,H1, est statistic, are incorrect. p-value & interpretation/conclusion are missing. (+1, -5) Part b assumptions are incorrect (-6) part c missing (-6) part d is incorrect (-6)

Solution

We have given the data.

The data contains Provider, TV, Phone.

Given that level of significance (a) = 0.05

Let mean for TV is µ1 and mean for Phone is µ2.

Here the hypothesis is,

H₀ : µ1 = µ2 Vs H₁ : µ1 µ2

Assumption :

Here we doesn\'t given population standard deviation so thats why we use t-test.

Data are independent.

The test statistic is,

First we check variances are equal or not.

The hypothesis for the test is,

H₀ : Variances are equal

H₁ : Variances are not equal.

number of observations for TV (n1) = 13

number of observations for Phone (n2) = 13

The test statistic is,

F = larger variance / smaller variance

acceptH0

Variances are equal.

We use pooled variance.

Sp = sqrt [ (n1-1)s1² + (n2 - 1)s2² / n1 + n2 - 2 ]

5.53022

Pooled variance Sp² = 30.58333

Pooled standard deviation = 5.53022

And the test statistic formula for testing two means are,

t = (X1bar - X2bar) / Sp * sqrt(1/n1 + 1/n2)

P-value < a(level of significance.

OR | t-statistic | > critical value

So we reject H₀ at 5% level of significance.

There is sufficient evidence of two difference in the mean rating between TV and Phone service are equal.

TV	Phone
74	78
74	83
70	77
68	72
67	74
66	81
64	75
64	73
62	71
61	70
60	71
59	71
54	63