A multinomial experiment produced the following results: Use Table 3. Category 1

Question

A multinomial experiment produced the following results: Use Table 3. Category 1 2 3 Frequency 139 120 71 a. Choose the appropriate alternative hypothesis at H0: p1 = 0.40, p2 = 0.40, and p3 = 0.20. All population proportions differ from their hypothesized values. At least one of the population proportions differs from its hypothesized value. b. Calculate the value of the test statistic at H0: p1 = 0.40, p2 = 0.40, and p3 = 0.20. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic c. Approximate the p-value. p-value < 0.005 p-value > 0.100 0.010 < p-value < 0.025 0.025 < p-value < 0.050 0.050 < p-value < 0.100 d. At 10% significance level, can we reject H0: p1 = 0.40, p2 = 0.40, and p3 = 0.20? Yes since the p-value is less than ?. Yes since the p-value is more than ?. No since the p-value is less than ?. No since the p-value is more than ?.

Explanation / Answer

applying chi square goodness of fit test:

value of the test statistic =1.84

c)  p-value : p-value > 0.100

d)No since the p-value is more than ?.

observed Expected Chi square category Probability(p) Oi Ei=total*p R2i=(Oi-Ei)2/Ei 1 0.400 139.000 132.0 0.37 2 0.400 120.000 132.0 1.09 3 0.200 71.000 66.0 0.38 total 1 330 330 1.841

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