Equities and bonds are two of the most traded asset classes. A financial analysist is interested to know the annual return rate performance between the equities and bonds. She randomly samples the annual return rate of equities and bonds. For a sample of 73 bonds, she found the mean rate was 18.72%, and the sample standard deviation was 3.55%. For a sample of 101 equities, she found the mean rate was 20.01%, and the sample standard deviation was 2.17%.

a. Test, at the 5% level, the null hypothesis that the population mean annual return rate for equities would be at most 18.

b. Test, at the 5% level, the null hypothesis that the population means are equal against the alternative that the population mean annual return rate is higher for equities than for bonds.