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 8181 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	18	14	12	18	19

Step 1 of 10: State the null and alternative hypothesis.

Choice 1:

H0: Service calls are equally distributed over the five working days.

Ha: Service calls are not equally distributed over the five working days.

Choice 2:

H0H0: Service calls are not equally distributed over the five working days.

HaHa: Service calls are equally distributed over the five working days.

Step 2 of 10:

What does the null hypothesis indicate about the proportions of service calls received each day?

Choice 1: The proportions of service calls received each day are all thought to be equal

Choice 2: The proportions of service calls received each day are different for each category (and equal to the previously accepted values).

Step 3 of 10:

State the null and alternative hypothesis in terms of the expected proportions for each category.

H0: Pi = ______

Ha: There is some difference amongst the proportions.

Step 4 of 10:

Find the expected value for the number of service calls received on Monday. Round your answer to two decimal places.

Step 5 of 10:

Find the expected value for the number of service calls received on Friday. Round your answer to two decimal places.

Step 6 of 10:

Find the value of the test statistic. Round your answer to three decimal places.

Step 7 of 10:

Find the degrees of freedom associated with the test statistic for this problem.

Step 8 of 10:

Find the critical value of the test at the 0.01 level of significance. Round your answer to three decimal places.

Step 9 of 10:

Make the decision to reject or fail to reject the null hypothesis at the 0.01 level of significance.

Choice 1: Fail to Reject Null Hypothesis

Choice 2:Reject Null Hypothesis

Step 10 of 10:

State the conclusion of the hypothesis test at the 0.01 level of significance.

Choice 1: There is not enough evidence to refute the claim that the service calls are distributed evenly among the days.

Choice 2: There is enough evidence to refute the claim that the service calls are distributed evenly among the days.

Answer 1

>> Step 1 of 10: The null and alternative hypothesis:

Choice 1:

H0: Service calls are equally distributed over the five working days.

Ha: Service calls are not equally distributed over the five working days.

>> Step 2 of 10: The null hypothesis indicate:

Choice 1: The proportions of service calls received each day are all thought to be equal.

>> Step 3 of 10: The null and alternative hypothesis in terms of the expected proportions for each category:

H0: Pi = 0.20

Ha: There is some difference amongst the proportions.

>> Step 4 of 10: The expected value for the number of service calls received on Monday

= 16.20

>> Step 5 of 10: The expected value for the number of service calls received on Friday

= 16.20

>> Step 6 of 10: The value of the test statistic

= 2.272

>> Step 7 of 10: The degrees of freedom associated with the test statistic for this problem

= 4

>> Step 8 of 10: The critical value of the test at the 0.01 level of significance

= 13.277

>> Step 9 of 10: The decision to reject or fail to reject the null hypothesis at the 0.01 level of significance:

Choice 1: Fail to Reject Null Hypothesis.

>> Step 10 of 10: The conclusion of the hypothesis test at the 0.01 level of significance:

Choice 1: There is not enough evidence to refute the claim that the service calls are distributed evenly among the days.

CALCULATIONS: