Question

A large supermarket carries four qualities of ground beef. Customers are believed to purchase these four varieties with probabilities of 0.06, 0.29, 0.18, and 0.47, respectively, from the least to most expensive variety. A sample of 517 purchases resulted in sales of 40, 147, 85, and 245 of the respective qualities. Does this sample contradict the expected proportions? Use α = .05.

(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 significant evidence of a difference from the expected proportions. Reject the null hypothesis, there is not significant evidence of a difference from the expected proportions.     Fail to reject the null hypothesis, there is significant evidence of a difference from the expected proportions. Fail to reject the null hypothesis, there is not significant evidence of a difference from the expected proportions.

You may need to use the appropriate table in Appendix B to answer this question.

Answer 1

Ans:

a)

	Observed,fo	pi	Expected,fe	(fo-fe)^2/fe
1	40	0.06	31.02	2.60
2	147	0.29	149.93	0.06
3	85	0.18	93.06	0.70
4	245	0.47	242.99	0.02
Total	517	1	517	3.37

Test statistic:

Chi square=3.37

ii)p-value bounds are 0.25 <p-value<0.35

p-value=CHIDIST(3.37,3)=0.3378

b)As,p-value is greater than 0.05,we do not reject null hypothesis.

Fail to reject the null hypothesis, there is not significant evidence of a difference from the expected proportions.