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 110 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	24	28	21	26	11

Step 3 of 9: 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 9: Find the expected value for the number of service calls received on Monday. Round your answer to two decimal places.

Step 5 of 9: Find the expected value for the number of service calls received on Wednesday. Round your answer to two decimal places.

Step 6 of 9: Find the value of the test statistic. Round your answer to three decimal places.

Step 7 of 9: Find the critical value of the test at the 0.1 level of significance. Round your answer to three decimal places.

Step 8 of 9: Make the decision to reject or fail to reject the null hypothesis at the 0.1 level of significance.

Step 9 of 9: State the conclusion of the hypothesis test at the 0.1 level of significance.

Answer 1

the necessary calculation table :-

hypothesis:-

proportion of all characters are equal,i.e, p_i = 1/5 = 0.2

at least one of the character has a different proportion

the necessary calculation table :-

days of week	observed	expected
mon	24	110*0.2= 22	(24-22)2/22 = 0.18182
tue	28	22	1.63636
wed	21	22	0.04545
thurs	26	22	0.72727
fri	11	22	5.5
	sum =110		sum= 8.0909

Step 3 : null and alternative hypothesis:-

[i.e, the expected proportions are equal for each days of week ] (claim)

There is some difference amongst the proportions.

Step 4 : the expected value for the number of service calls received on Monday = 22

Step 5 : the expected value for the number of service calls received on Wednesday = 22

Step 6:the value of the test statistic is:-

Step 7 : the critical value of the test at the 0.1 level of significance = 7.779

[ df =(5-1) = 4

chi square critical value for df=4,alpha=0.10 is = 7.779 ]

Step 8 : decision : reject the null hypothesis.

[ chi square calculated = 8.091 > 7.779 ]

Step 9 :conclusion:  

there is enough evidence to refute the telephone company's claim that the number of service calls does not change from day-to-day.

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