You are given the following summary statistics from a sample of 50 observations:

Question

You are given the following summary statistics from a sample of 50 observations: (use Table 3): a. Using the Jarque-Bera test, specify the null and alternative hypotheses to determine whether or not the data are normally distributed. H_0: S = 0 and K = 0: H_A: S notequalto 0 and K notequalto 0 H_0: S = 0 and K= 0: H_A: S 0 b. At the 5% significance level, what is the critical value? (Round the answer to 3 decimal places.) c. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) d. What is the conclusion? Reject H_0: there is not enough evidence to support the claim that the data are not normally distributed. Reject H_0: there is enough evidence to support the claim that the data are not normally distributed. Do not reject H_0: there is not enough evidence to support the claim that the data are not normally distributed. Do not reject H_0: there is enough evidence to support the claim that the data are not normally distributed.

Explanation / Answer

SOLUTIONB:

CRITICAL VALUE=5.99

for alpha=0.05 and with chi sq and 2 degrees of freedom

SOLUTIONC:

JB=n.[S2/6 +K2 /24]

n=sample size

S=skewness

K=kurtosis

JB=50(1.12^2/6+1.63^2/24)

JB=15.99

SolutionD:

JB test stat>Critical value

15.99>5.99

Reject Null hypothesis

Reject Ho there is enough evidence to support the claim that the data are not normally distributed

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