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

Solution:-

Output from the excel is given below:

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis H₀: σ_Traditional² σ_Prepaid²

Alternative hypothesis H_A: σ_Traditional² σ_Prepaid²

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data. Using sample data, the degrees of freedom (DF), and the test statistic (F).

DF₁ = n₁ - 1 = 10 -1

D.F₁ = 9

DF₂ = n₂ - 1 = 13 -1

D.F₂ = 12

Test statistics:-

F = 1.5184

Since the first sample had the larger standard deviation, this is a right-tailed test.

p value for the F distribution = 0.246

Interpret results. Since the P-value (0.246) is greater than the significance level (0.05), we failed to reject the null hypothesis.

From the above test there is insufficient evidence to conclude that there is a difference in the variability of the satisfaction rating between the types of cellphone providers.

The steps for excel to perform the test is:

1) Click on "DATA" in tool bar.

2) Then select "Data Analysis".

3) Then select "F-Test Two sample for varainces"

4) Fill the data range in the Pop up box

5) Then click on "OK"