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 80 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	14	17	27	15	7

Step 1 of 10:

H0: Service calls are not equally distributed over the five working days.

Ha: 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?

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

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

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 Tuesday. 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

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.

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

Answer 1

Step 1 of 10:

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

Step 3 of 10:

Ho: Pi =0.2

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 =80*0.2 =16

Step 5 of 10: Find the expected value for the number of service calls received on Tuesday=80*0.2 =16

Step 6 of 10:  

Applying chi square test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
Mon	0.200	14	16.00	-0.50	0.250
Tue	0.200	17	16.00	0.25	0.063
Wed	0.200	27	16.00	2.75	7.563
Thu	0.200	15	16.00	-0.25	0.063
Fri	0.200	7	16.00	-2.25	5.063
total	1.000	80	80		13.000

  value of the test statistic.=13.000

Step 7 of 10:

degree of freedom =categories-1=

4

Step 8 of 10:

for 0.025 level and 4 degree of freedom :critical value =

11.143

Step 9 of 10:

Reject Null Hypothesis

Step 10 of 10:

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