A school board is investigating two different academic programs. $20$ students from each program were given the same exam, and the mean score was reported for Program A and Program B$.$ A $95\%$ T confidence interval for the difference in mean exam score $($assuming equal variances$)$ is reported as

$(-10\mathrm{.}524,-0\mathrm{.}476)$

$($a$)$ What is the observed difference in mean exam score between Program A and Program B$?$

$0$

$5\mathrm{.}024$

$-0\mathrm{.}476$

$-5\mathrm{.}5$

$-10\mathrm{.}524$

Points possible: $2$

$($b$)$ What is the estimate of pooled standard deviation that was used to create this interval? $($In the case of rounding errors, chose the closest option$)$

$9\mathrm{.}423$

$2\mathrm{.}482$

$18\mathrm{.}847$

$7\mathrm{.}845$

Points possible: $2$

$($c$)$ Had a confidence interval been constructed instead, the interval would be guaranteed to not cover $0.$

Had a confidence interval been constructed instead, the interval might cover $0.$