10.57 According to the Insurance Information Institute, the mean annual expendit
ID: 2960103 • Letter: 1
Question
10.57 According to the Insurance Information Institute,the mean annual expenditure for automobile insurance for
U.S. motorists is $706. Suppose that a government official
in North Carolina has surveyed a simple random sample
of 80 residents of her state, and that their auto insurance
expenditures for the most recent year are in data file
XR10057. Based on these data, examine whether the mean
annual auto insurance expenditure for motorists in North
Carolina might be different from the $706 for the country
as a whole. Identify and interpret the p-value for the test.
Using the 0.05 level of significance, what conclusion do
you reach?
File XR10057:
Expense
729
940
953
678
532
828
627
812
799
618
598
920
558
853
633
650
665
549
788
451
964
783
881
742
784
883
638
769
971
765
686
928
639
597
568
934
844
618
602
893
722
827
706
855
479
873
647
957
751
678
611
721
774
824
910
882
653
811
696
1008
859
805
878
628
740
760
596
993
539
512
744
852
504
702
663
672
647
669
767
581
Explanation / Answer
H0: mean = 706 Ha: mean NOT = to 706 mean :739.575 standard dev: 136.0511608 t test statistic: 2.207286785 The p-value with df=n-1=79 and 2 tails is: 0.030195 thats less than the significance 0.05, so reject the null hyp. and derive that the mean is different from 706
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