This is a two-tailed test. With a sample size greater than 30, using a z-test is acceptable. The test statistic = = ?2.5. For a two-tailed z-test, the critical values are ±1.645 for a 10% significance level, ±1.96 for a 5% significance level, and ±2.58 for a 1% significance level. The researcher should reject the hypothesis at the 10% and 5% significance levels, but fail to reject the hypothesis at the 1% significance level.

Using Student's t-distribution, the critical values for 60 degrees of freedom (the closest available in a typical table) are ±1.671 for a 10% significance level, ±2.00 for a 5% significance level, and ±2.66 for a 1% significance level. The researcher should reject the hypothesis at the 10% and 5% significance levels, but fail to reject the hypothesis at the 1% significance level.

This is a one-sided alternative because of the "greater than" belief.

If a researcher is trying to show that a return is greater than the risk-free rate then this should be the alternative hypothesis. The null hypothesis would then take the form of a less than or equal to statement.

The alternative hypothesis is typically the hypothesis that a researcher hopes to support after a statistical test is carried out. We can reject or fail to reject the null, not 'prove' a hypothesis.

This is a one-sided alternative because of the “less than” belief. We expect to reject the null.

This is a one-sided alternative because of the “greater than” belief. We expect to reject the null.

The most common set of hypotheses will take the form of an equal to statement for the null and a not equal to statement for the alternative.

An appropriate null hypothesis is one that the researcher wants to reject. If Patterson believes that the returns on Mondays are greater than on other days, he would like to reject the hypothesis that the opposite is true–that returns on Mondays are not greater than returns on other days.