Question

9. The police department in Madison, Connecticut released the following numbers of calls for the different days of the week for a February that has 28 days: Monday (114), Tuesday (152), Wednesday (160), Thursday (164), Friday (179), Saturday (196), Sunday (130). Use a 0.01 level of significance to test the claim that the different days of the week have the same frequency of phone calls. a. Write the null and alternative hypotheses. Label the claim. b. Draw the graph and shade the critical area(s). Place the critical value(s) on the graph.

Answer 1

a)

null hypothesis is(claim)

7 Ho: p1 = P2 = P3 = P4 = ps = po = pz = The alternative hypothesis states the opposite of the null hypothesis: H.: At least one of the pi's is different.

b)

The x(chi-square) distribution with v = 6 degrees of freedom 0.16 p=0.0000 v=6 0.14 0.12 0.10 f(x) 0.08 0.06 0.04 0.02 0.00 0 29.814 42

c)

Categories Observed Expected (fo-fe)2/fe Category 1 114 1095*0.142857=156.428 (114-156.428)2/156.428 11.508 Category 2 152 1095*0.142857=156.428 (152-156.428)2/156.428 = 0.125 Category 3 160 1095*0.142857=156.428 (160-156.428)2/156.428 0.082 Category 4 164 1095*0.142857=156.428 (164-156.428)2/156.428 = 0.366 Category 5 179 1095*0.142857=156.428 (179-156.428)2/156.428 = 3.257 Category 6 196 1095*0.142857=156.428 (196-156.428)2/156.428 = 10.01 Category 7 130 1095*0.142857=156.428 (130-156.428)2/156.428 = 4.465 Sum = 1095 1095 29.814

Based on the information provided, the significance level is a = 0.01, the number of degrees of freedom is df = 7-1=6, so then the rejection region for this test is R={x?: x² > 16.812}

The Chi-Squared statistic is computed as follows: 72 x? (O; - E) Ei 11.508 + 0.125 + 0.082 +0.366 +3.257 + 10.01 + 4.465 = 29.814

If X is a random variable having a distribution with v = 6 degrees of freedom, then p = Pr[X > 29.814] = 0.0000.

d)

Since it is observed that x = 29.814 > xě = 16.812, it is then concluded that the null hypothesis is rejected.

e)

There is sufficient evidence to reject the claim that the difference days of the week have the same frequency.