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 111 randomly selected service calls was conducted. Is there enough evidence to refute the telephone company's claim that the number of service calls does not change from day-to-day?

Days of the Week Mon Tue Wed Thu Fri
Number of Calls 15 21 26 31 18

A. State the null and alternate hypothesis

Answer 1

To check if there's enough evidence to refute the claim that service calls are equally distributed among the weekdays, we must conduct a hypothesis test using a Chi-square goodness-of-fit test based on the observed call frequencies as compared to the expected frequencies if the calls were equally distributed.

Step-by-step explanation:

To determine if there is enough evidence to refute the telephone company's claim that service calls are equally distributed among the five working days of the week, we need to set up a hypothesis test. The null and alternative hypotheses are:

• Null hypothesis (H0): The number of service calls is equal for all working days.
• Alternative hypothesis (Ha): The number of service calls is not equal for all working days.

A Chi-square goodness-of-fit test would be appropriate for this scenario. If the service calls are equally distributed, we would expect 111/5 = 22.2 calls approximately for each day (Monday through Friday). However, the observed frequencies are 15, 21, 26, 31, and 18 for Monday to Friday respectively. After calculating the Chi-square statistic and comparing it to the critical value from the Chi-square distribution table with the appropriate degrees of freedom (df=4), we can determine whether to reject the null hypothesis.

If the calculated Chi-square value is greater than the critical value, there is sufficient evidence at a given significance level to reject the null hypothesis and conclude that the number of service calls is not equally distributed among the workdays.