Question

In: Statistics and Probability

A recent article found that Massachusetts residents spent an average of $860.70 on the lottery in...

A recent article found that Massachusetts residents spent an average of $860.70 on the lottery in 2010, more than three times the U.S. average (http://www.businessweek.com, March 14, 2012). A researcher at a Boston think tank believes that Massachusetts residents spend significantly less than this amount. He surveys 100 Massachusetts residents and asks them about their annual expenditures on the lottery.

a. Specify the competing hypotheses to test the researcher’s claim.

b. Specify the critical value(s) of the test at the 10% significance level.

c. Compute the value of the appropriate test statistic.

d. At α = 0.10, what is the conclusion?

Annual Lottery Expenditures (in $) 790 594 899 1105 1090 1197 413 803 1069 633 712 512 481 654 695 426 736 769 877 777 785 776 1119 833 813 747 1244 1023 1325 719 1182 528 958 1030 1234 833 745 985 774 1002 561 681 546 777 844 856 785 1289 502 703 334 1140 594 719 1002 943 1025 969 576 627 989 915 662 802 876 962 878 668 1227 947 864 1016 1022 723 665 1072 610 538 992 978 1291 1139 1111 873 850 941 845 639 495 1016 939 974 893 645 1098 788 682 686 764 759

Solutions

Expert Solution

:-   Massachusetts residents spent an average of $860.70

Number Values
1 790 2697.764
2 594 61474.244
3 899 3255.844
4 1105 69200.564
5 1090 61533.764
6 1197 126067.604
7 413 183989.524
8 803 1516.324
9 1069 51556.244
10 633 43655.924
11 712 16884.404
12 512 108860.404
13 481 130277.684
14 654 35321.444
15 695 21591.364
16 426 173006.084
17 736 11223.284
18 769 5320.244
19 877 1229.204
20 777 4217.204
21 785 3242.164
22 776 4348.084
23 1119 76762.244
24 833 79.924
25 813 837.524
26 747 9013.604
27 1244 161652.244
28 1023 32782.724
29 1325 233346.964
30 719 15114.244
31 1182 115640.804
32 528 98558.324
33 958 13469.924
34 1030 35366.564
35 1234 153711.044
36 833 79.924
37 745 9397.364
38 985 20466.164
39 774 4615.844
40 1002 25619.204
41 561 78927.284
42 681 25901.684
43 546 87580.484
44 777 4217.204
45 844 4.244
46 856 197.684
47 785 3242.164
48 1289 199862.644
49 502 115559.204
50 703 19304.324
51 334 258003.044
52 1140 88839.764
53 594 61474.244
54 719 15114.244
55 1002 25619.204
56 943 10213.124
57 1025 33510.964
58 969 16144.244
59 576 70724.084
60 627 46199.204
61 989 21626.644
62 915 5337.764
63 662 32378.404
64 802 1595.204
65 876 1160.084
66 962 14414.404
67 878 1300.324
68 668 30255.124
69 1227 148271.204
70 947 11037.604
71 864 486.644
72 1016 30296.884
73 1022 32421.604
74 723 14146.724
75 665 31307.764
76 1072 52927.604
77 610 53796.164
78 538 92379.524
79 992 22518.004
80 978 18512.324
81 1291 201654.884
82 1139 88244.644
83 1111 72393.284
84 873 964.724
85 850 64.964
86 941 9812.884
87 845 9.364
88 639 41184.644
89 495 120367.364
90 1016 30296.884
91 939 9420.644
92 974 17439.844
93 893 2607.124
94 645 38785.364
95 1098 65566.724
96 788 2909.524
97 682 25580.804
98 686 24317.284
99 764 6074.644
100 759 6879.044
Total 84194 4668367.640

Mean   

Standard deviation   

S = 217.1525

To Test

H0 :-  

Massachusetts residents spend more than average on the lottery

H1 :-  

Massachusetts residents spend less than average on the lottery

Test Statistic :-

Test Criteria :-

Reject null hypothesis if t < -

Critical value  

- 0.8639 > - 1.290, We fail to reject null hypothesis

Conclusion :- We Accept Null Hypothesis

There is no sufficient evidence to conclude that the average spend of Massachusetts residents on lottery is significantly less than $860.70.

orchestra answered 2 years ago
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