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.

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

Let 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.

Formulate for your own purposes (so no need to supply it as part of the answer) the null and alternative hypotheses consistent with testing whether any difference exists between the mean returns on the S&P 500 and small- cap stocks.

Is it true or false that we reject the null hypothesis at the 0.05 significance level for the January 1960 to December 1979 subperiod