Question

A random sample of n1=19 securities in Economy A produced mean returns of x̄ 1=5.5% with s1=2.1% while another random sample of n2=18 securities in Economy B produced mean returns of x̄ 2=4.5% with s2=1.9%. At α =0.05, can we infer that the returns differ significantly between the two economies?

a. Calculate the test statistic. t= 0.000 Round to three decimal places if necessary

b. Determine the critical value(s) for the hypothesis test. + Round to three decimal places if necessary

c. Conclude whether to reject the null hypothesis or not based on the test statistic.

Reject

Fail to Reject

Answer 1

Solution:

Given:

securities in Economy A:

n₁=19

x̄ ₁=5.5%

s₁=2.1%

securities in Economy B :

n₂=18

x̄ ₂=4.5%

s₂=1.9%

α =0.05

We have to test if we can infer that the returns differ significantly between the two economies.

Thus hypothesis are:

Part a. Calculate the test statistic.

where

thus

Part b)  Determine the critical value(s) for the hypothesis test.

df= n1 + n2 - 2

df = 19 +18 - 2

df = 35

two tail area = level of significance =α =0.05

Since df = 35 is not listed in t table, we look for its previous df = 30

thus t critical values = ( -2.042 , 2.042 )

If exact values needed then use Excel command:

=T.INV.2T(alpha , df)

=T.INV.2T(0.05,35)

=2.030

thus t critical values : ( -2.030, 2.030)

Part c) Conclude whether to reject the null hypothesis or not based on the test statistic.

Decision Rule:

Reject null hypothesis H0, if absolute t test statistic value > t critical value = 2.030, otherwise we fail to reject H0.

Since absolute t test statistic value = t = 1.516 < t critical value = 2.030, we fail to reject H0.

Thus correct answer is:

Fail to Reject