Question

An investor believes that investing in domestic and international stocks will give a difference in the mean rate of return. They take two random samples of 15 months over the past 30 years and find the following rates of return from a selection of domestic (Group 1) and international (Group 2) investments. Can they conclude that there is a difference at the 0.10 level of significance? Assume the data is normally distributed with unequal variances. Use a confidence interval method. Round to 4 decimal places.

Average Group 1 = 2.1234, SD Group 1 = 4.8765, n1 = 15

Average Group 2 = 3.0945, SD Group 2 = 5.1115, n2 = 15

______ < μ₁ - μ₂ < __________

Answer 1

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: ​

Ha:

We need to construct the 90% confidence interval for the difference between the population means μ1​−μ2​, for the case that the population standard deviations are not known. The following information has been provided about each of the samples:

Therefore, based on the data provided, the 90% confidence interval for the difference between the population means μ1​−μ2​ is −4.0664<μ1​−μ2​<2.1242, which indicates that we are 90% confident that the true difference between population means is contained by the interval (-4.0664, 2.1242).

Since the confidence interval contains 0,  there is not enough evidence to claim that the population mean μ1​ is different than μ2​, at the 0.10 significance level.

Graphically

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