Question

A​ walk-in medical clinic believes that arrivals are uniformly distributed over weekdays​ (Monday through​ Friday). The table below shows the observed frequency of arrivals based on the averages obtained from random samples of 5 Mondays, 5 Tuesdays, and so on. On Mondays, for example, the clinic received an average of 25 patients. It also shows the expected frequency of arrivals, based on the uniform distribution.

x = Day of week	Observed Frequency	Expected Frequency
Monday	25	20
Tuesday	22	20
Wednesday	19	20
Thursday	18	20
Friday	16	20
Total	100	100

Assume that a​ goodness-of-fit test is to be conducted using a 0.10 level of​ significance.

(Note: this would be a good problem to practice on the calculator, and check your work on Excel.)

Identify the chi-square test statistic and critical value, and state the result of the X2 GOF test.

		With a test statistic of 9.24 and a critical value of 11.74, we will fail to reject the null, and conclude there is not sufficient evidence that arrivals do not follow a uniform distribution.
		With a test statistic of 7.78 and a critical value of 2.50, we will reject the null, and conclude there is sufficient evidence that arrivals do not follow a uniform distribution.
		With a test statistic of 9.24 and a critical value of 7.78, we will reject the null, and conclude there is sufficient evidence that arrivals do not follow a uniform distribution.
		With a test statistic of 2.50 and a critical value of 7.78, we will fail to reject the null, and conclude there is not sufficient evidence that arrivals do not follow a uniform distribution.

Answer 1

Oi	Ei	(Oi-Ei)^2/Ei
25	20	1.25
22	20	0.2
19	20	0.05
18	20	0.2
16	20	0.8
100
	TS	2.5
	critical value	7.78
	p-value	0.644635793

TS = 2.5 ,

critical value = =CHISQ.INV(0.9,4) = 7.78

TS < critical value , we fail to reject the null

option D) With a test statistic of 2.50 and a critical value of 7.78, we will fail to reject the null, and conclude there is not sufficient evidence that arrivals do not follow a uniform distribution

is correct

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