Question

In: Statistics and Probability

10.45 Is there a difference in the variance of the satisfaction rating of traditional cellphone providers...

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

Solutions

Expert Solution

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 F9,12,.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


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