A/ln order to conduct a hypothesis test for the population variance, you compute

Question

A/ln order to conduct a hypothesis test for the population variance, you compute s^2 = 75 from a sample of 21 observations drawn from a normally distributed population. Use the critical value approach to conduct the following test at alpha = 0.10 H_0: sigma^2 lessthanorequalto 50; H_1: sigma^2 > 50 b/Consider a multinomial experiment with n = 400 and k = 3. The null hypothesis is H_0: p_1 = 0.60, p_2 = 0.25, and p_3 = 0.15. The observed frequencies resulting from the experiment are At the 5% significance level, what is the conclusion to the hypothesis test?

Explanation / Answer

T = (21-1)(75/50) = 30

Reject the null hypothesis that the variance is a specified value, 02, if

20.9,20 = 28.412

T>20.9,20 , therefore reject the null hypotheses, there is sufficient evidence to conclude that the variance is not equal to 50.

b) H0 : p1 = 0.6 , p2 = 0.25, p3 = 0.15
Ha: Atleast one p is not equal to its specified value

A goodness-of-fit test is used to test the hypothesis that an observed frequency distribution fits (or conforms to) some claimed distribution

Expected frequency, ei = n*pi
e1 = 400*0.6 = 240, e2 = 400*0.25 = 100, e3 = 400*0.15 = 60

Test statistic, X2 = (Oi - Ei)2/Ei = (250-240)2/240 + (94-100)2/100 + (56-60)2/60 = 1.043333

Degree of freedom, DF = K-1 = 3-1 = 2

The P-Value is 0.59354. The result is not significant at p < 0.05. Fail to reject the null hypothesis

a) Test Statistic: T=(N1)(s/0)2

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