A large supermarket carries four qualities of ground beef. Customers are believe

Question

A large supermarket carries four qualities of ground beef. Customers are believed to purchase these four varieties with probabilities of 0.07, 0.26, 0.1, and 0.57, respectively, from the least to most expensive variety. A sample of 503 purchases resulted in sales of 50, 159, 76, and 218 of the respective qualities. Does this sample contradict the expected proportions? Use = .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 < ________

Explanation / Answer

50 / 503 = 0.099

159 / 503 = 0.316

76 / 503 = 0.151

218 / 503 = 0.43

X^2 = ( 0.099 - 0.07)^2 / 0.07 + (0.316 - 0.26)^2 / 0.26 + (0.151-0.1)^2 / 0.1 + (0.43 - 0.57)^2 / 0.57

X^2 = 0.012+0.012+0.026+0.034

X^2 = 0.084

p value : 0.995 < p < 0.99

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