Consider a multinomial experiment with n = 360 and k = 3. The null hypothesis is

Question

Consider a multinomial experiment with n = 360 and k = 3. The null hypothesis is H0: p1 = 0.60, p2 = 0.25, and p3 = 0.15. The observed frequencies resulting from the experiment are (Use Table 3): Category 1 2 3

Frequency 230 80 50

a. Choose the appropriate alternative hypothesis. All population proportions differ from their hypothesized values. At least one of the population proportions differs from its hypothesized value.

b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic

b-2. Approximate the p-value. p-value < 0.005 p-value > 0.100 0.010 < p-value < 0.025 0.050 < p-value < 0.100 0.005 < p-value < 0.010

c. At the 1% significance level, what is the conclusion to the hypothesis test? Reject H0 since the p-value is less than ?. Reject H0 since the p-value is more than ?. Do not reject H0 since the p-value is less than ?. Do not reject H0 since the p-value is more than ?.

Explanation / Answer

a. Here the appropriate alternative hypothesis is that "At least one of the population proportions differs from its hypothesized value"

b. Here n= 360 and k = 3

X2 = 2.31 Here,

dF = k - 1= 3 - 1= 2

Here p - value = 0.3143

so here p - value > 0.100

(c) at 1% significance level,  Do not reject H0 since the p-value is more than ?.

Category Observed Expected Proportion Expected (O -E)^2/E 1 230 0.6 216 0.9074 2 80 0.25 90 1.1111 3 50 0.15 54 0.2963 Sum 360 1 360 2.31

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