The number of murders by day of week in New Jersey during 2011 and 2003 is shown
ID: 3230525 • Letter: T
Question
The number of murders by day of week in New Jersey during 2011 and 2003 is shown in the table below. For the 2011 data, perform a significance test to test the null hypothesis that a murder is equally likely to occur on any given day. Again, for the 2011 data perform a significance test of the null hypothesis that murders happen on each weekday with equal probability, similarly on the weekends, but not necessarily with the same probability. For each test, write down explicitly the null and alternative hypothesis.Explanation / Answer
1.
Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: No. Of murder 2003
Using category names in day
Test Contribution
Category Observed Proportion Expected to Chi-Sq
Sun 53 0.142857 47 0.76596
Mon 42 0.142857 47 0.53191
Tue 51 0.142857 47 0.34043
Wed 45 0.142857 47 0.08511
Thurs 36 0.142857 47 2.57447
Fri 37 0.142857 47 2.12766
Sat 65 0.142857 47 6.89362
N DF Chi-Sq P-Value
329 6 13.3191 0.038
P-value < 0.05 so we reject null hypothesis. we conclude that murder is likely to on any given day.
2.
Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: No. of murder 2011
Using category names in day
Test Contribution
Category Observed Proportion Expected to Chi-Sq
Sun 63 0.142857 54.4286 1.34983
Mon 53 0.142857 54.4286 0.03750
Tue 50 0.142857 54.4286 0.36033
Wed 51 0.142857 54.4286 0.21597
Thurs 55 0.142857 54.4286 0.00600
Fri 53 0.142857 54.4286 0.03750
Sat 56 0.142857 54.4286 0.04537
N DF Chi-Sq P-Value
381 6 2.05249 0.915
P-value >0.05 so we do not reject null hypothesis. we conclude that murder is'nt likely to on any given day.