Question

random sample of n1=17securities in Economy A produced mean returns of x̄ 1=5.8% with s1=2.5% while another random sample of n2=20 securities in Economy B produced mean returns of x̄ 2=4.6% with s2=2.2%.. At α =0.1 , can we infer that the returns differ significantly between the two economies?

Assume that the samples are independent and randomly selected from normal populations with equal population variances ( σ 1²= σ 2²)

T-Distribution Table

________________________________________

a. Calculate the test statistic.

t=

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

a.

Test Statistics

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

b.

Rejection Region

Based on the information provided, the significance level is α=0.1, and the degrees of freedom are df=35. In fact, the degrees of freedom are computed assuming that the population variances are equal.

Hence, it is found that the critical value for this two-tailed test is tc​=1.690, for α=0.1 and df=35.

The rejection region for this two-tailed test is

c.

Fail to Reject

Since it is observed that ∣t∣=1.553≤tc​=1.69, it is then concluded that the null hypothesis is not rejected.

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