Question

A telephone company claims that the service calls which they receive are equally distributed among the five working days of the week. A survey of 130 randomly selected service calls was conducted. Is there enough evidence at 0.05 level of significance to refute the telephone company's claim that the number of service calls does not change from day-to-day? Interpret your result.

Days of the Week Mon Tue Wed Thu Fri Number of Calls 30 25 30 31 14

                

Answer 1

Let denote the observed and expected frequency of service calls received by the service company on five working days of the week. The company claims that the service calls which they receive are equally distributed among the five working days of the week, i.e No. of calls received per day = 130 / 5 = 26.

Here, E_i = 26, i = 1,2,3,4,5.

We are asked to test whether the observed frequencies in the sample of 130 calls are the same as what is expected.

To test: Vs   

The appropriate statistical test to test the above hypothesis would be a Chi-square test of Goodness of fit, where we test whether the observed distribution is the same as the expected. The test statistic is given by:

where k = No. of values; with rejection region of the test given by,

Here, k = 5. Hence for 5 - 1 = 4 degrees of freedom, at 0.05 level of significance, the critical value of the test can be obtained from the chi-square table as:

We may reject he null hypothesis, if the test statistic

Substituting the values in the test statistic:

= 7.769

Since the test statistic does not lie in the rejection region, we fail to reject the null hypothesis at 5% level. We may conclude that the data does not provide sufficient evidence to refute the telephone company's claim that the number of service calls does not change from day-to-day.