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 8080 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	1919	1212	1313	1717	1919

Copy Data

Step 1 of 10:

State the null and alternative hypothesis.

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

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

or

H0H0: Service calls are equally distributed over the five working days.

HaHa: Service calls are not 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?

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

or
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.

Ho:Pi=

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 Thursday. 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 0.0250.025 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 0.0250.025 level of significance.

Fail to Reject Null Hypothesis

or

Reject Null Hypothesis

Step 10 of 10:

State the conclusion of the hypothesis test at the 0.0250.025 level of significance.

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

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

Answer 1

1)null and alternative hypothesis.

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

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

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

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

3) H₀:P_i= 1/5 = 0.2

H₁ : at least one P_i not equal to 0.2.

4) Expected number of service calls on Monday = 0.2*8080 = 1616.00

5) Expected number of service calls on Thursday = 0.2*8080 = 1616.00

6)

	Observed	Expected	Difference	Difference Sq.	Diff. Sq. / Exp Fr.
Mon	1919	1616	303.00	91809.00	56.81
Tue	1212	1616	-404.00	163216.00	101.00
Wed	1313	1616	-303.00	91809.00	56.81
Thur	1717	1616	101.00	10201.00	6.31
Fri	1919	1616	303.00	91809.00	56.81
					277.750

test statistic Chi^2 value is 277.75.

7) degrees of freedom = 5-1 = 4

8) the critical value of the test at the 0.025 level of significance = 11.143

9) Since test statistic is greater than critical value we reject null hypothesis.

10) There is enough evidence to refute the claim that the service calls are distributed evenly among the days.