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  Â	  B  Â	  C  Â	  D  Â	  E  Â
4.5	6.9	4.4	6.3	5.2
3.9	6.9	3.8	6.4	5.5
4.1	7.1	3.9	6.3	4.5
3.7		4.3		5.3

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


(ii) Find the p-value. (Give your answer bounds exactly.)
< p <
(b) State the appropriate conclusion.

Reject the null hypothesis, there is not significant evidence of a difference in mean fills. Reject the null hypothesis, there is significant evidence of a difference in mean fills.     Fail to reject the null hypothesis, there is significant evidence of a difference in mean fills. Fail to reject the null hypothesis, there is not significant evidence of a difference in mean fills.

Answer 1

(a) The test statistic: F= 62.67

(ii) P-value (0.0000): P< 0.001

(b) Conclusion:

Reject the null hypothesis, there is significant evidence of a difference in mean fills.