In: Statistics and Probability
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.
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 |
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/s22
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