PSY 520 Topic 7 Exercises Answers/ GCU PSY 520

PSY 520 Topic 7 Exercises 19.9 Randomly selected records of 140 convicted criminals reveal that their crimes were committed on the following days of the week: (a) Using the .01 level of significance, test the null hypothesis that in the underlying population, crimes are equally likely to be committed on any day of the week. 1 Statistical Hypothesis: H0 = Psun = Pmon = Ptues = Pwed = Pthurs = Pfri = Psat = 7 H1 : H0 is false Decision Rule: Reject H0 at the 0.01 level of significance = x2 > 16.81 fe = (expected proportion) (total sample size) frequency Mon Tues Wed Thurs Fri Sat Sun Total f fe 20 20 140 Null Hypothesis: f 0−fe X2 = ∑ (¿¿ fe) 2 ¿ ( 17−20) 2 = { ( 21−20) 2 + + ( 22−20) 2 + (18−20 )2 + (23−20) 2 ( 24−20 )2 + + 20 ( 15−20) 2 20 } 9 = 20 + 1 20 + 4 20 + 4 20 + 9 20 + 16 25 20 + 20 68 = 20 = 3.4 The null hypothesis is returned at the 0.01 level because the observed x2 of 3.4 is < the critical x2 of 16.81 The result is that crimes are likely to be committed on any day of the week. (b) Specify the approximate p -value for this test result. The null hypothesis H0 is returned at the 1% level of significance, which indicates that p > 0.01. The x2 table values indicate the value 12.6 at the 0.05 level and degrees of freedom =6. The null hypothesis can be retained at the 5% level, so p>0.05. How might this result be reported in the literature