Question

1. The following data on annual rates of return were collected from five stocks listed on the New York Stock Exchange (“the big board”) and five stocks listed on NASDAQ. Assume the population standard deviations are the same. At the .10 significance level, can we conclude the annual rates of return are higher on the big board?

NYSE                  17.16                   17.08                 15.51                  8.43                     25.15

NASDAQ             15.80                  16.28                  16.21                  17.97                   7.77

Really important: Use Excel as described in “How to perform two-sample hypothesis tests” in the content area to do this problem. Be sure to save the Excel file and send it to me, named as specified I the instructions to this test.

a. State the null and alternate hypotheses. Ho:u1 ≤u2 Ha:u1>u2

b. Select alpha. 0.10, 1.645

c. Select the test statistic.

d. Formulate the decision rule.

e. What is the value of the test statistic? t= 0.579

f. Determine and interpret the effect size and p-value.

g. Draw conclusions based on statistical and practical significance.

ANSWER a-g Please and thank you!

Answer 1

Output using excel:

t-Test: Two-Sample Assuming Equal Variances
	NYSQ	NASDAQ
Mean	16.666	14.806
Variance	35.39043	16.16203
Observations	5	5
Pooled Variance	25.77623
Hypothesized Mean Difference	0
df	8
t Stat	0.57926
P(T<=t) one-tail	0.289178
t Critical one-tail	1.396815
P(T<=t) two-tail	0.578356
t Critical two-tail	1.859548

a)

Null and Alternative hypothesis:

Ho : µ1 ≤ µ2

H1 : µ1 > µ2

b)

Alpha = 0.10

c)

Test used = pooled two sample t test.

d)

Critical value, t crit = ABS(T.INV(0.1, 8)) = 1.397

Reject Ho if t > 1.397

e)

Pooled variance :

S²p = ((n1-1)*s1² + (n2-1)*s2² )/(n1+n2-2) = 25.7762

Test statistic:

t = (x̅1 - x̅2) / √(s²p(1/n1 + 1/n2 ) = 0.5793

f)

Cohen's d = (x̅1- x̅2)/√s²p = 0.366

df = n1+n2-2 = 8

p-value = T.DIST.RT(0.5793, 8) = 0.2892

g)

p-value > α, Do not reject the null hypothesis

Conclusion:

There is not enough evidence to conclude that the annual rates of return are higher on the big board at 0.10 significance level.