Question

Are phone calls equally likely to occur any day of the week? The day of the week for each of 651 randomly selected phone calls was observed. The results are displayed in the table below. Use an a = 0.05 significance level. a. Complete the rest of the table by filling in the expected frequencies: Frequencies of Phone Calls for Each Day of the Week Outcome Frequency Expected Frequency Sunday 90 Monday 93 Tuesday 97 Wednesday 79 Thursday 89 Friday 111 Saturday 92 b. What is the correct statistical test to use? Select an answer c. What are the null and alternative hypotheses? H: The distribution of phone calls is uniform over the days of the week. Phone calls and days of the week are independent. The distribution of phone calls is not uniform over the days of the week. Phone calls and days of the week are dependent.

Answer 1

93 We have Observed Expected Outcome Frequency (Oi) Frequency (Ei) (0;-E;) Sunday 90 9 Monday 93 93 0 Tuesday 97 93 16 Wednesday 79 93 196 Thursday 89 93 16 Friday 111 93 324 Saturday 93 TOTAL 651 (0,-E;) E 0.0968 0.0000 0.1720 2. 1075 0.1720 3.4839 0.0108 6.0430 92 1 b. The correct statistical test is Chi-square test for goodness of fit C. The null hypotheses is Ho: the distribution of phones calls is uniform over the days of the week and the alternative is H1: the distribution is not uniform (0; - E) The test statistic is x2 = = 6.0430 E the p-value is PCX>6.0430)=0.4184 since p-value is greater than the significance level, there is not sufficient information in the sample to reject the null hypothesis