Question

The following frequency distribution shows the monthly stock returns (in percent) for Home Depot for the years 2003 through 2007. (You may find it useful to reference the appropriate table: chi-square table or F table)

Monthly Returns	Observed Frequency
Less than -5	13
-5 up to 0	16
0 up to 5	20
5 or more	11
	n = 60

SOURCE: www.yahoo.finance.com.

Over this time period, the following summary statistics are provided:

Mean	Median	Standard Deviation	Skewness	Kurtosis
0.31%	0.43%	6.49%	-0.15	-0.38

a-1. Choose the null and alternate hypotheses.

H₀: The monthly stock returns follow a normal distribution with a mean of 0.31% and a standard deviation of 6.49%.; H_A: The monthly stock returns do not follow a normal distribution with a mean of 0.31% and a standard deviation of 6.49%.

H₀: The monthly stock returns do not follow a normal distribution with a mean of 0.31% and a standard deviation of 6.49%.; H_A: The monthly stock returns follow a normal distribution with a mean of 0.31% and a standard deviation of 6.49%.

a-2. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Test statistic _____________?

a-3. Find the p-value.

p-value < 0.01

0.01 ? p-value < 0.025

0.025 ? p-value < 0.05

0.05 ? p-value < 0.10

p-value ? 0.10

a-4. Can you conclude that monthly returns do not follow the normal distribution at the 5% significance level?

Yes since the p-value is more than ?.

Yes since the p-value is less than ?.

No since the p-value is less than ?.

No since the p-value is more than ?.

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

Test Statistic = 0.586

b-2. Find the p-value.

p-value < 0.01

0.01 ? p-value < 0.025

0.025 ? p-value < 0.05

0.05 ? p-value < 0.10

p-value ? 0.10

b-3. Can you conclude that monthly returns do not follow the normal distribution at the 5% significance level?

No since we do not reject H₀.

Yes since we reject H₀.

Yes since we do not reject H₀.

No since we reject H₀.

I actually only need help with the test statistic below a-2.   Already figured out the rest of the question but wanted to post the whole question just in case. As for the a-2 test statistic I keep on getting 27.047, but showing up incorrect.  

Answer 1

a-1)

H₀: The monthly stock returns follow a normal distribution with a mean of 0.31% and a standard deviation of 6.49%.; H_A: The monthly stock returns do not follow a normal distribution with a mean of 0.31% and a standard deviation of 6.49%.

a-2)

Applying chi square tesT:

Class Limits				observed	Normal	Normal	Expected	χ2=(O-E)2/E
lower		Upper	Bin	frequency(O)	probabilty	probabilty(p)	frequency(E=p*ΣO)
	-	-5	--5	13	P(X<-5)	0.2061	12.37	0.032
-5	-	0	-5-0	16	P(-5<X<0)	0.2740	16.44	0.012
0	-	5	0-5	20	P(0<X<5)	0.2841	17.05	0.510
5	-		5-	11	P(5<X<)	0.2358	14.15	0.701
			Total	60		1.0000	60.01	1.256

Test statistic =1.256 (please try 1.257 if this comes wrong)

p value >0.10

b-1)

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

0.586

b-2) p value >0.1

b-3)

No since we do not reject H₀.