Question

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

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

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.

Please provide step by step solutions for excel.

Answer 1

for Traditional telephone proider

The sample size is n=10. The provided sample data along with the data required to compute the sample variance are shown in the table below:

	Traditional	Traditional2
	89	7921
	88	7744
	79	6241
	78	6084
	76	5776
	73	5329
	73	5329
	70	4900
	68	4624
	67	4489
Sum =	761	58437

the sample variance is

for PrePaid telephone provider.

The sample size is n=13. The provided sample data along with the data required to compute the sample variance are shown in the table below:

	PrePaid	PrePaid2
	87	7569
	85	7225
	84	7056
	80	6400
	79	6241
	78	6084
	76	5776
	76	5776
	75	5625
	74	5476
	70	4900
	70	4900
	66	4356
Sum =	1000	77384

the sample variance is

for testing if there is a difference in the variance of the satisfaction rating of traditional cellphone provider who bill for service at the end of a month (often under a contract) and prepaid cellphone service providers who bill in advance without a contract we use F test.

The provided sample variances are and the sample sizes are given by

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

This corresponds to a two-tailed test, for which a F-test for two population variances needs to be used.

(2) Rejection Region

Based on the information provided, the significance level is and the rejection region for this two-tailed test is

(3) Test Statistics

The F-statistic is computed as follows:

(4) Decision about the null hypothesis

Since from the sample information we get that, it is then concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population variance traditional telephone provider​ is different than the population variance prepaid telephone provider​, at the significance level.