Question

Are phone calls equally likely to occur any day of the week? The day of the week for each of 700 randomly selected phone calls was observed. The results are displayed in the table below. Use an a=0.01 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 112 Monday 120 Tuesday 115 Wednesday 87 Thursday 73 Friday 91 Saturday 102 b. What is the correct statistical test to use? Select an answer c. What are the null and alternative hypotheses? HO: The distribution of phone calls is not uniform over the days of the week. Phone calls and days of the week are independent Phone calls and days of the week are dependent The distribution of phone calls is uniform over the days of the week.

Answer 1

Solution Given data n=700 L= 0.01 (a) To Compute the grest of the table by filling in the expected farequencies Frequencies of Phone calls for Each of the week Outcome Frequency Expected Frequency Sunday Too 7 100 112 Monday loo 700 7 Tuesday Too 115 loo Wednesday 700 87 - loo Thursday 73 700 - loo Friday 700 90 T = loo 102 Saturday 700 = 100 (6) Here we have to use che square test for goodness of fit.

x² (12) 2 (20)2 (15) (-13) (-27) 2 uniform answer. (c) To state the hall and alter native hypothesis Nun hypothesis Ho : The distribution of phone calls is unifom over the days of the week Therefore the option -D" is the correct answer Alternative hypothesis H,: The distribution of Phone calls is not over the days of the week. Therefore the lloption - Ah is the correct (2) Now to find the degrees of freedom degrees of freedom af = 7-1 1df = 6 Now to find the test statistic We know that test statistic is given by E (ci-Fi)? K-1 The formula of 2 (12-10) (120-6) (115-100) 2 (115-100) 2 (87-100) ² (73-100)? (91-100) + + t loo Too Too 100 Too Too (102-100) 2 7 Too t + + + Q2 Too Гоо foo loo + Too loo ſoo 169 729 81 + 400 Too + + t 225 loo x? 144 loo + + 100 foo 4 roo foo

x= 1.44 +4 + 2.257 1.697 7.29+ 0.81+ 0.044 X= 14.520 The test statistic for this data es 17.520 (f) Nou to find the degrees of freedom degrees of freedom =K-1 of 17-1 df = 6 Now to find the P-value p-value = 0.0076 0.0076 The p-value for this Sample (g) The p-value is less than a (h) Based on this, we should reject the null hypothesis (Ho) (i) Thus, the final conclusion is There is sufficient evidence to distribution of Phone Calls is over the days of the week Therefore the option-A" is the correct answer. Conclude that the not uniform