Question

10.45 Is there a difference in the variance of the satisfaction rating of traditional cellphone providers who bill for service at the end of a month (often under contract) and prepaid cellphone service providers who bill in advance without a contract? The file CellphoneProviders contains the satisfaction rating for 10 traditional cellphone providers and 13 prepaid cellphone service providers.

1. At the 0.05 level of significance, is there evidence of a difference in the variability of the satisfaction rating between the types of cellphone providers?
2. Determine the p-value in (a) and interpret its meaning.
3. What assumption do you need to make in (a) about the two populations in order to justify your use of the F test?
4. Based on the results of (a) and (b), which t test defined in section 10.1 should you use to compare the mean satisfaction rating of the two types of cellphone providers?

CellPhone Provider	Type	Rating
Consumer Cellular	Traditional	89
Ting	Traditional	88
Grat Cell/Jitterbug	Traditional	79
Credo Mobile	Traditional	78
Virgin Mobile	Traditional	76
U. S. Cellular	Traditional	73
T-Mobile	Traditional	73
Verizon Wireless	Traditional	70
AT&T	Traditional	68
Sprint	Traditional	67
Republic Wireless	PrePaid	87
Cricket	PrePaid	85
Page Plus Cellular	PrePaid	84
Straight Talk	PrePaid	80
TracFone	PrePaid	79
MetroPCS	PrePaid	78
Virgin Mobile	PrePaid	76
Net10	PrePaid	76
Boost Mobile	PrePaid	75
T-Mobile	PrePaid	74
Verizon Wireless	PrePaid	70
AT&T	PrePaid	70
Sprint	PrePaid	66

Answer 1

A)Null Hypothesis:The variances of the two groups are the same

Alternative hypothesis: The variances of the two groups differ from each other

The test statistic is F = s₁²/s₂^{​​​​​​2}

The value is 1.518

The critical value is F_9,12,.05= 2.7964

Since the calculated value is less than the critical value, we accept the null hypothesis and conclude that there is no evidence that there is variability of the satisfaction rating of two cell phone providers

B)p value is 0.2458

Since p value is greater than .05,we accept the null hypothesis and the interpretation follows from A

C)Assumptions of F test for test of 2 variances

The populations from which the two samples are drawn are approximately normally distributed.
The two populations are independent of each other.

D)Since there are 2 independent groups , the test to be used here is two sample independent t test which can be used to test mean satisfactory rating of cell phone providers