Suppose that an economist believes a certain macro-finance model for stock marke

Question

Suppose that an economist believes a certain macro-finance model for stock market as a true model. This model gives her a prediction that the U.S. average annual real return for equity (=stock) is 2.5 percent. The sample data for 1889-1988 (100 years), however, gives her the sample mean 6.5 percent and sample variance 256 percent squared. If we can allow probability of the Type I error to be up to 5 percent, would you advise her to keep using the model? Justify your advice using statistical analysis.

Explanation / Answer

Here we have given population mean = 2.5, sample size = 100, sample mean = 6.5 sample standard deviation = 16.

(I deliberately ignore the percent unit for the calculation purpose only).

population standard deviation is not known. So we used one sample t - test for testing of hypothesis.

Null hypothesis : Ho: The model gives average annual real return for equity is 2.5.

Alternative hypothesis H1: The model does not gives average annual real return for equity is 2.5.

Solve this problem by using MINITAB, follow the procedure:

Choose Stat > Basic Statistics > 1-Sample t.

In Summarized data enter Sample size, mean, and standard deviation .

Check Perform hypothesis test. In Hypothesized mean, enter 2.5.

Click Options. In Confidence level, enter 95. Click OK in each dialog box.

Session window output

MTB > Onet 100 6.5 16;
SUBC>   Test 2.5.

One-Sample T

Test of mu = 2.5 vs not = 2.5

N      Mean StDev    SE Mean    95% CI          T       P
100   6.50    16.00       1.60         (3.33, 9.67)    2.50 0.014

Decision rule: 1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.014 < 0.05 so we used first rule.

That is we reject null hypothesis and accept alternative hypothesis.

Conclusion: At 5% level of significance there are sufficient evidence to say that the model does not gives average annual real return for equity is 2.5.

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