Question

You are given the following summary statistics from a sample of 26 observations: (You may find it useful to reference the appropriate table: chi-square table or F table) Mean 67.28 Standard Deviation 11.73 Skewness 1.11 Kurtosis 1.78

a. Using the Jarque-Bera test, specify the null and alternative hypotheses to determine whether or not the data are normally distributed.

H0: S = 0 and K = 0;

HA: S ≠ 0 and K ≠ 0

H0: S = 0 and K = 0;

HA: S < 0 and K < 0

H0: S = 0 and K = 0;

HA: S > 0 and K > 0

b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

b-2. Find the p-value.

0.01 p-value < 0.025

p-value < 0.01

p-value 0.10

0.05 >-p-value < 0.10

0.025 p-value < 0.05

c. What is the conclusion at the 1% significance level? Do not reject H0; there is not enough evidence to support the claim that the data are not normally distributed. Reject H0; there is enough evidence to support the claim that the data are not normally distributed. Reject H0; there is not enough evidence to support the claim that the data are not normally distributed. Do not reject H0; there is enough evidence to support the claim that the data are not normally distributed.

Answer 1

a)

H0: S = 0 and K = 0;

HA: S ≠ 0 and K ≠ 0

b-1)

S=	1.11
K=	1.78
n=	26

test statistic X2 =(n/6)*(S2+K2/4) =

8.772

b-2)

0.01 p-value < 0.025

c)

Do not reject H0; there is not enough evidence to support the claim that the data are not normally distributed.