Question

You found that three grocery stores having the following market shares: A=.35, B=.50, C=.15. You survey 500 people to see if the market shares have changed and you find the data below. Use the Chi-squared goodness of fit test and ?=.05. A—150 B—250 C—100.

Answer 1

(1) The Hypothesis

H0: The market shares is distributed as follows A - 35%, B = 50% and C = 15%.

Ha: The distribution differs from that stated in the null hypothesis.

The Test Statistic

Each Expected value = (% / 100) * N. N = 500

	Observed	Expected %	Expected	(O-E)2	(O-E)2/E
Share A	150	35	175	625	3.57140
Share B	250	50	250	0	0.00000
Share C	100	15	75	625	8.33330
Total	500.00	100.00	500.00		11.905

Test = 11.91

The Critical value at = 0.05 (default level), df = n – 1 = 2 is 5.992

The p value at Test = 11.91 is 0.0026

(4) The Decision Rule: If test is > critical, then Reject H0.

If p value is < , Then Reject H0.

(5) The Decision: Since test (11.91) is <> critical (5.992), We Reject H0.

Since p value (0.0026) is < (0.05), We Reject H0.

(6) The Conclusion: There is sufficient evidence at the 95% significance level to conclude that the distribution is different from that as stated (A = 35%, B = 50%, C = 15%).