Question

5. A large supermarket carries four qualities of beef. Customers are believed to purchase these four qualities with probabilities of 0.10, 0.30, 0.35, and 0.25, respectively, from the least to most expensive. A sample of 500 purchases resulted in sales of 48, 162, 191, and 99 of respective qualities. Does this sample contradict the expected proportions? Use a) α = 0.05 b) α =0.025

Answer 1

Hypothesis:

H0 : Distribution of sample is same as provided probabilities.

Ha : Distribution of sample is different than provided one.

We use chi-square goodness of fit test to test this hypothesis.

Observation table:

Oi	Pi	Ei=Npi	(Oi-Ei)^2 / Ei
48	0.1	50	0.08
162	0.3	150	0.96
191	0.35	175	1.46285714
99	0.25	125	5.408
N=500			7.91085714

Test statistic,

Degrees of freedom = n-s-k-1 = 4-0-0-1 = 3

Critical value at 0.05 level of significance = 7.82

Since calculated value is greater than critical value we reject null hypothesis and conclude that sample contradict the expected proportions.

Critical value at 0.025 level of significance = 9.348

Since calculated value is less than critical value we accept null hypothesis and conclude that sample does nit contradict the expected proportions.