# A large supermarket carries four qualities of ground beef. Customers are believed to purchase these four varieties with probabilities of 0.13, 0.16, 0.13, and 0.58, respectively, from the least to most expensive variety.

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Question: A large supermarket carries four qualities of ground beef. Customers are believed to purchase these four varieties with probabilities of 0.13, 0.16, 0.13, and 0.58, respectively, from the least to most expensive variety. A sample of 482 purchases resulted in sales of 46, 151, 88, and 197 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.)

(b) Find the p-value. (Give your answer bounds exactly.)
____< p < ____

A large supermarket carries four qualities of ground beef.

Customers are believed to purchase these four varieties with probabilities of 0.13, 0.16, 0.13, and 0.58, respectively, from the least to most expensive variety.

Sample size = n  = 482

and observed counts of purchases resulted in sales as 46, 151, 88, and 197

We have to test if  this sample contradict the expected proportions.

Level of significance = 0.05

Thus hypothesis would be:

H0: p1 = 0.13, p2 =0.16, p3= 0.13, p4 = 0.58

H1: this sample contradict the expected proportions.

Part a) Find the test statistic

Since we have to test if sample or observed counts are same as expected counts, we use Chi-square test of goodness of fit test.