The table below gives data on the monthly returns on the S&P 500 and small-cap stocks for the period January 1960 through December 1999 and provides statistics relating to their mean differences.

Let μ d stand for the population mean value of difference between S&P 500 returns and small-cap stock returns. Use a significance level of 0.05 and suppose that mean differences are approximately normally distributed.
A. Formulate null and alternative hypotheses consistent with testing whether any difference exists between the mean returns on the S&P 500 and small-cap stocks.
B. Determine whether or not to reject the null hypothesis at the 0.05 significance level for the January 1960 to December 1999 period.
C. Determine whether or not to reject the null hypothesis at the 0.05 significance level for the January 1960 to December 1979 sub-period.
D. Determine whether or not to reject the null hypothesis at the 0.05 significance level for the January 1980 to December 1999 sub-period.

Differences S&P 500 Small-Cap Stock Return (%) (S&P 500 Small-Cap Stock) Measure Return (%) January 1960-December 1999, 480 months Mean 1.0542 1.3117 -0.258 Standard deviation 4.2185 5.9570 3.752 January 1960-December 1979, 240 months Mean 0.6345 1.2741 -0.640 Standard deviation 4.096 4.0807 6.5829 January 1980-December 1999, 240 months Mean 1.3492 1.4739 0.125 Standard deviation 4.3197 5.2709 3.339