Question

Use Minitab to answer the questions. Make sure to copy all output from the Minitab:

1.   Followings Tables shows previous 11 months stock market returns.

Date	Monthly SP500 Return	Monthly DJIA Return
12/7/2007	-0.8628	-0.7994
1/8/2008	-6.1163	-4.6323
2/8/2008	-3.4761	-3.0352
3/8/2008	-0.5960	-0.0285
4/8/2008	4.7547	4.5441
5/8/2008	1.0674	-1.4182
6/8/2008	-8.5962	-10.1937
7/8/2008	-0.9859	0.2468
8/8/2008	1.2191	1.4548
9/8/2008	-9.2054	-6.0024
10/8/2008	-16.8269	-4.8410

1. Let’s consider the population mean of SP500 as µ1 and that of DJIA as µ2 while none of population variance is known. Test following hypothesis:

Ho : µ1 = µ2

Ha :   µ1 ≠ µ2

2. Let’s consider the population variance of SP500 as σ²₁ and that of DJIA as σ²₂, and none of them are known. Test following hypothesis:

Ho :   σ²₁ = σ²₂

Ha :   σ²₁ ≠ σ²₂

6) Perform the following hypothesis test

Ho :   σ²₁ ≤ σ²₂

Ha :   σ²₁ > σ²₂

Answer 1

1) We have to test ,

Ho : µ1 = µ2

Ha :   µ1 ≠ µ2

Calculation using Minitab:-

Two-sample T for SP vs DJIA

N Mean StDev SE Mean
SP 11 -3.60 6.13 1.8
DJIA 11 -2.25 4.05 1.2

Difference = μ (SP) - μ (DJIA)
Estimate for difference: -1.36
95% CI for difference: (-6.03, 3.32)
T-Test of difference = 0 (vs ≠): T-Value = -0.61 P-Value = 0.548 DF = 17

Result:- Here p-value is greater than alpha=0.05. Hence we accept the null hypothesis.

Hence we say that, population mean of SP500 is same as population mean of DJIA . I.e. µ1 = µ2

2) We have to check,

Ho :   σ²₁ = σ²₂

Ha :   σ²₁ ≠ σ²₂

_{Calculation using Minitab :-}

_{Minitab output,}

_Method

_{Null hypothesis All variances are equal
Alternative hypothesis At least one variance is different
Significance level α = 0.05}

_{95% Bonferroni Confidence Intervals for Standard Deviations}

_{Sample N StDev CI
SP 11 6.13058 (4.08177, 11.7826)
DJIA 11 4.05017 (2.69662, 7.7842)}

_{Individual confidence level = 97.5%}

_Tests

_{Test
Method Statistic P-Value
F 2.29 0.207}

Result :-

Here p-value is greater than alpha=0.05. Hence we accept the null hypothesis.

Hence we say that, population variance of SP500 is equal as population variance of DJIA . i.e. σ²₁ = σ²₂