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 f0 17 21 22 18 23 24 15 140 fe 20 20 20 20 20 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 20 20 20 20 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 p0.05. How might this result be reported in the literature