Question

In: Statistics and Probability

An article found that Massachusetts residents spent an average of $860.70 on the lottery in 2010,...

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

Expenditures
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

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

  • H0: μ = 860.70; HA: μ ≠ 860.70

  • H0: μ ≥ 860.70; HA: μ < 860.70

  • H0: μ ≤ 860.70; HA: μ > 860.70

b-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

b-2. Find the p-value.

  • p-value < 0.01

  • 0.01 ≤ p-value < 0.025

  • 0.025 ≤ p-value < 0.05

  • 0.05 ≤ p-value < 0.10

  • p-value ≥ 0.10

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

  • Reject H0; there is insufficient evidence to state that the average Massachusetts resident spent less than $860.70 on the lottery in 2010

  • Reject H0; there is sufficient evidence to state that the average Massachusetts resident spent less than $860.70 on the lottery in 2010

  • Do not reject H0; there is sufficient evidence to state that the average Massachusetts resident spent less than $860.70 on the lottery in 2010

  • Do not reject H0; there is insufficient evidence to state that the average Massachusetts resident spent less than $860.70 on the lottery in 2010

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Expert Solution

orchestra answered 1 year ago
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