$7\mathrm{.}43$ Buy$-$side vs$.$ sell$-$side analysts' earnings forecasts. Refer to the Financial Analysts Journal $($July$/$August $2008)$ study of earnings forecasts of buy$-$side and sell$-$side analysts, Exercise $2\mathrm{.}86($p$.105).$ Recall that data were collected on $3,526$ forecasts made by buy$-$side analysts and $58,562$ forecasts made by sell$-$side analysts, and the relative absolute forecast error was determined for each. A positive forecast error indicates that the analyst is overestimating earnings, while a negative forecast error implies that the analyst is underestimating earnings. Summary statistics for the forecast errors in the two samples are reproduced in the table below.

$\backslash$table$[[,$Buy$-$Side Analysts,Sell$-$Side Analysts$],[$Mean$,0\mathrm{.}85,-0\mathrm{.}05],[$Standard$,1\mathrm{.}93,0\mathrm{.}85],[$Deviation$,,]]$

Source: Based on B$.$ Groysberg, P$.$ Healy, and C$.$ Chapman, "Buy$-$Side vs$.$ Sell$-$Side Analysts' Earnings Forecast," Financial Analysts Journal, Vol. $64,$ No$.4,$ July$/$August $2008.$

a$.$ Conduct a test $($at $=\mathrm{.}01)$ to determine if the true mean forecast error for buy$-$side analysts is positive. Use the observed significance level $(p-$value$)$ of the test to make your decision and state your conclusion in the words of the problem.

b$.$ Conduct a test $($at $=\mathrm{.}01)$ to determine if the true mean forecast error for sell$-$side analysts is negative.