11.2: Tests of Means and p-values

Question 1

Why doesn’t statistical significance imply economic significance? State the 3 factors.

Answer 1

Statistical significance does not imply economic significance because:

1. Transaction costs
2. Taxes
3. Risk

These factors make committing funds to a strategy unattractive, even though the statistical evidence of positive returns is highly significant.

Question 2

What is p-value? What is the p-value for one-tailed test? Two-tailed? Provide an example.

Answer 2

P-value is the probability of obtaining a test statistic that would lead to a rejection of the null hypothesis, assuming the null hypothesis is true. It is the smallest level of significance for which the null hypothesis can be rejected.

For one-tailed tests, the p-value lies above the computed test statistic for upper tail tests or below the computed test statistic for lower tail tests.

For two-tailed tests, the p-value is the probability that lies above the positive value of the computed test statistic plus the probability that lies below the negative value of the computed test statistic.

Example: For a two-tailed hypothesis test about the mean value of a random variable at 95% significance level where….

Question 3

What is the critical z-value for 10% significance level?

Answer 3

Two-tailed test = +/- 1.65

One-tailed test = +/- 1.28

Question 4

What is the critical z-value for 5% significance level?

Answer 4

Two-tailed test = +/- 1.96

One-tailed test = +/- 1.65

Question 5

What is the critical z-value for 1% significance level?

Answer 5

Two-tailed test = +/- 2.58

One-tailed test = +/- 2.33