A consultant for a company recommends an$$ "employee athlete"$$ program, encouraging every employee to devote $5$ minutes an hour to physical activity. The company worries that the gains in productivity will be offset by the loss in time on the job.$$ They'd like to know if the program increases or decreases productivity. To measure$$ it$,$ they monitor a random sample of $190190$employees$,$ measuring their hourly keystrokes both before and after the program is instituted. Complete parts a through c$.$

Keystrokes per Hour

Before

After

Difference

left parenthesis After minus Before right parenthesis$($After$$Before$)$

Mean

$1527\mathrm{.}21527\mathrm{.}2$

$1543\mathrm{.}91543\mathrm{.}9$

$16\mathrm{.}716\mathrm{.}7$

SD

$169\mathrm{.}5169\mathrm{.}5$

$149\mathrm{.}4149\mathrm{.}4$

$92\mathrm{.}792\mathrm{.}7$

N

$190190$

$190190$

$190190$Give a$95\%$ confidence interval for the mean change in productivity$($as measured by keystrokes per$$ hour$).$

left parenthesis nothing comma nothing right parenthesisenter your response here,enter your response here