Private DormsRus & On Campus DormFreshman's Weight Gain

Data Analysis

Learning Team BDeshone Jones, Rosalyn Young

Elena Rist, Bridget Lyles, Jimmie McFarland

Freshmen’sChange in Weight Data

• The data set contains the weight of freshmen both before and after their first semester at a leading state university. The freshmen lived in either an on-campus dorm (O), or a private off-campus dorm managed by DormsRUs (D), who claims their students have a healthier lifestyle.

Female Data Collection: Q1

• The data set contains the change in weight of female freshmen’s after their first semester at a leading state university. The freshmen’s lived in either an on-campus dorm (O), or a private off-campus dorm managed by DormsRUs (D), who claims their students have a healthier lifestyle.

Research Questions/Hypothesis• Q1. Do the female freshmen’s on campus

gain less than the weight of females freshmen’s at DormsRus?

• H0:o = d

Ha: o < d

Descriptive statistics

(O) Change in weight (D) change in weight count 18 18 mean 2.50 -0.11 sample standard deviation 2.07 1.28 sample variance 4.26 1.63 minimum -1 -3 maximum 7 3 range 8 6

population variance 4.03 1.54 population standard deviation 2.01 1.24

standard error of the mean 0.49 0.30

confidence interval 95.% lower 1.47 -0.75 confidence interval 95.% upper 3.53 0.52 half-width 1.03 0.64

-2 -1 0 1 2 3 4 5 6 7 8

BoxPlot-F

(O) Change in weight

-4 -3 -2 -1 0 1 2 3 4

BoxPlot-F

(D) change in weight

-2 -1 0 1 2 3 4 5 6 7 8

DotPlot-F

(O) Change in weight

-4 -3 -2 -1 0 1 2 3 4

DotPlot-F

(D) change in weight

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0-2 0 2 4 6 8

Normal Curve Plot-F

Normal Score

(O) C

hang

e in

wei

ght

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0-4

-2

0

2

4

Normal Curve Plot-F

Normal Score

(D) c

hang

e in

wei

ght

-1 0 1 2 3 4 5 6 7 8 0

10203040

Histogram-F

(O) Change in weight

Perc

ent

-3 -2 -1 0 1 2 3 4 0

102030405060

Histogram-F

(D) change in weight

Perc

ent

Hypothesis Test: Paired ObservationsSmall Sample Test Solution (t-test)

We want to compare the private off campus female freshman's to the DormRus female freshman weight gain. We will sample 18 female freshman = .05 level of significance.

• 2.500 mean (o) Change in weight• -0.111 mean (d) Change in weight• 2.611 mean difference (o) change in weight – (d) change in weight• 2.913 std. dev.• 0.687 std. error • 18 n 95% confidence level 1.162 lower 4.060 upper• .9993 p-value (one-tailed, lower) t= 3.803

t-3 -2 -1 0 1 2 -3

-1.740

Probability T-Distribution

t-distribution df=17

P(lower) P(upper).0500 .9500

Reject H0

.05

Critical Value (s): t= 3.803Not in rejection region

Also P= .9993>.05

Decision & Conclusion

• Q1

• Reject at = .05• There is evidence that show the on campus

freshman females gained more weight than DormRus female freshman's

• On campus female freshman's gained 2.389 lbs more than DormsRus female freshman's.

Female/Male Data Collection: Q2

• The data set contains the change in weight of female/male freshmen’s after their first semester at a leading state university. The freshmen’s lived in either an on-campus dorm (O), or a private off-campus dorm managed by DormsRUs (D), who claims their students have a healthier lifestyle.

Research Questions/Hypothesis

• Q2. Do the freshmen’s (Male/Female) on campus gain less than the weight than of freshmen’s (Male/Female) at DormsRus?

• H0:o = d

Ha: o < d

Descriptive statistics

(O) change in weight (D) change in weight count 33 33 mean 2.88 -0.36 sample standard deviation 1.85 1.62 sample variance 3.42 2.61 minimum -1 -4 maximum 7 3 range 8 7

population variance 3.32 2.53 population standard deviation 1.82 1.59

standard error of the mean 0.32 0.28

confidence interval 95.% lower 2.22 -0.94 confidence interval 95.% upper 3.53 0.21 half-width 0.66 0.57

-2 -1 0 1 2 3 4 5 6 7 8

BoxPlot-F/M

(O) change in weight

-5 -4 -3 -2 -1 0 1 2 3 4

BoxPlot-F/M

(D) change in weight

-2 -1 0 1 2 3 4 5 6 7 8

DotPlot-F/M

(O) change in weight

-5 -4 -3 -2 -1 0 1 2 3 4

DotPlot-F/M

(D) change in weight

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0-5

0

5

10

Normal Curve Plot-F/M

Normal Score(O) c

hang

e in

wei

ght

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0-6 -4 -2 0 2 4

Normal Curve Plot-F/M

Normal Score

(D) c

hang

e in

wei

ght

-1 0 1 2 3 4 5 6 7 8 05

1015202530

Histogram-F/M

(O) change in weight

Perc

ent

-4 -3 -2 -1 0 1 2 3 4 05

1015202530

Histogram-F/M

(D) change in weight

Perc

ent

Hypothesis Test: Independent Groups (z-test)

We want to compare the on campus freshman's to the private DormRus freshman weight gain. We will sample 33 freshman = .05 level of significance.• 2.879 mean (o) Change in weight• -0.364 mean (d) Change in weight• 3.242 mean difference (o) change in weight – (d) change in weight• 2.705 std. dev.• 0.471 std. error • 33 n 95% confidence level 2.320 lower 4.165 upper• 1.0000 p-value (one-tailed, lower) z= 6.89

Decision & Conclusion

• Q2

• Reject at = .05• There is evidence that show the on campus

freshman females/males gained more weight than DormRus females/males.

• On campus female freshman's gained 2.515 lbs. more than DormsRus females/male freshman's.

t-3 -2 -1 0 1 2 -3

-1.694

Probability T-Distribution

t-distribution df=32

P(lower) P(upper).0500 .9500

Reject H0

.05

Critical Value (s): z= 6.89Not in rejection region

Also P= 1.0000>.05

Conclusion

• DormsRus initial claim was that there students were healthier, based on the data collection evidence shows the claim is true.