$(1)$ In the first part of this project, you want to test if$,$ before the introduction of caloric labeling, the daily

caloric intake by students dining in dining halls A and B was indeed similar. To do this, start by

calculating the number of students surveyed at each dining hall. In cell F$2,$ input the number of

students surveyed in dining hall A; in cell G$2,$ input the number of students surveyed in dining hall B$.$

$($HINT: use the COUNTIF function in Excel$).$ Calculate sample mean of the caloric intake for

students dining in A and B$.$ Input your results in cells F$3$ and G$3$ respectively. Calculate the observed

sample variance of the caloric intake for students dining in A and B$.$ Input your results in cells F$4$ and

G$4$ respectively. $($Use the VAR.S function in Excel$).$

$(2)$ In cell F$6,$ calculate the pooled variance. $($HINT: Check page $24$ of Chapter$\_8\_$Slides$).$

$(3)$ Using t$-$value for a $95\%$ confidence interval as well as the pooled variance derived in the previous

step, calculate the confidence limits for the mean difference in daily caloric intake in dining halls A

and B before the introduction of caloric labeling. Input your t$-$value in cell F$7,$ your lower confidence

limit in cell F$8,$ and your upper confidence limit in cell G$8.$ Does your confidence interval include $0?$

Answer $$YES$$ or $$NO$$ in cell H$8.($HINT: Use the T$.$INV$\mathrm{.}2$T function in Excel to help you derive

the appropriate t$-$value; Check page $25$ of Chapter$\_8\_$Slides$).$

$(4)$ In the second part of the project, you want to test if the daily caloric intake by students dining in

dining hall A changed after the introduction of caloric labeling; thus, for elements $(4)$ through $(6),$

only include in your calculations the students dining in dining hall A$.$ In column D $($cells starting

with D$2),$ calculate the difference in caloric intake before and after introduction of labelling for each

student in dining hall A $($define the difference as the caloric intake after minus the caloric intake

before$).$ Calculate point estimate for the population mean paired difference and input it in cell F$11.$

$($Although this element will not be graded directly, these are necessary calculations for other elements

that will be graded.$)$

$(5)$ In cell F$13,$ calculate the sample standard deviation of the difference. $($Use the STDEV.S function in

Excel$).$

$(6)$ Using t$-$value for a $95\%$ confidence interval, calculate the confidence limits for the difference in

means between the daily caloric intake in dining hall A before and after the introduction of caloric

labeling. Input your t$-$value in cell F$14,$ your lower confidence limit in cell F$15,$ and your upper

confidence limit in cell G$15.$ Does your confidence interval include $0?$ Answer $$YES$$ or $$NO$$ in

cell H$15.($HINT: Use the T$.$INV$\mathrm{.}2$T function in Excel to help you derive the appropriate t$-$value;

Check page $7$ of Chapter$\_8\_$Slides$).$