Question

A certain vending company's soft-drink dispensing machines are supposed to serve 6 oz of beverage. Various machines were sampled, and the resulting amounts of dispensed drink (in ounces) were recorded, as shown in the following table. Does this sample evidence provide sufficient reason to reject the null hypothesis that all five machines dispense the same average amount of soft drink? Use α= .01?

Machines
A	B	C	D	E
4.1	7.2	4.0	6.3	5.7
3.8	7.0	4.2	6.4	4.8
3.9	6.9	4.2	6.4	6.0
3.9		4.6		6.2

(a) Find the test statistic. (Give your answer correct to two decimal places.)


(ii) Find the p-value. (Give your answer bounds exactly.)

Answer 1

H0: There is no significance difference among the means of 5 machines dispense

H1: There is significance difference among the means of 5 machines dispense

Given los be  α= .01

From the given data

	1	2	3	4
Machine					Total (Ti.)	Ti.^2/ni
A	4.1	3.8	3.9	3.96	15.76	62.0944
B	7.2	7	6.9		21.1	148.4033333
C	4	4.2	4.2	4.6	17	72.25
D	6.3	6.4	6.4		19.1	121.6033333
E	5.7	5.8	6	6.2	23.7	140.4225
				G =	96.66	544.7735667

Here P-value < alpha so we reject H0

Thus we conclude that there is significance difference among the means of 5 machines dispense