College administrators across the country have become very concerned after noticing an increase in the number of deaths in college students from binge drinking. Several psychological studies have indicated the source of this issue is different for men versus women college students. The college administrators conducted a study that consisted of a random selection of 500 college students and classifying the students into one of four categories:
1: Male that is a frequent binge drinker (more than twice a week)
2: Male that is not a frequent binge drinker
3: Female that is a frequent binge drinker
4: Female that is not a frequent binge drinker
College administrators believe the percentages are 15, 30, 25, 30. After taking a random sample of 500 college students, they obtain the following results:
Category

# of Students

1: Male that is a frequent binge drinker

75

2: Male that is not a frequent binge drinker

125

3: Female that is a frequent binge drinker

100

4: Female that is not a frequent binge drinker

200

Type a short report (1/2 page  1 page) of the results of your findings and attach relevant statistical analysis output (for example excel/SPSS/written analysis). Include in your report:
a) The test you choose to run and why
b) Results of the test of their hypothesis (using a = 0.05) (be sure to write this in layman's terms, not statnerd lingo)
c) Test statistic, associated degrees of freedom, pvalue
d) Calculate by hand the value of the test statistic (your clients do not trust computers)
2) In the second phase of Dr. Shotwell's research, she is measuring the older adult's total fitness score (this is calculated by totaling measurements made regarding things like the individual's coordination, time to climb steps, reaching ability, etc.) She wishes to compare two living conditions (1 = "assisted living"; 2 = "community dwelling") in terms of the individual's total fitness score. In particular, her hypothesis is that the mean total fitness score for individuals living in community dwellings will be higher than the mean total fitness score for individuals living in assisted living homes. She randomly samples 28 individuals and obtains the following data:
Individual

Living Condition

Total Fitness Score

1

2

254.00

2

2

246.00

3

2

250.00

4

2

250.00

5

2

242.00

6

2

260.00

7

2

256.00

8

2

261.00

9

1

222.00

10

2

236.00

11

1

218.00

12

1

240.00

13

2

257.00

14

1

238.00

15

1

246.00

16

1

232.00

17

1

228.00

18

1

180.00

19

1

220.00

20

2

251.00

21

2

246.00

22

2

264.00

23

2

264.00

24

2

262.00

25

2

202.00

26

1

177.00

27

1

236.00

28

1

252.00

In response to Dr. Shotwell's 1^{st} research question, please provide the following in a typed ½ page report that includes the following: attach relevant statistical analysis output (for example excel/SPSS/written analysis).
a) The type of statistical test you choose to run and why?
b) Results of your test in terms of Dr. Shotwell's hypothesis (mean total fitness score for those living in community dwelling is more than the mean total fitness score for those in assistedliving homes). Include the value of relevant test statistics and associated degrees of freedom, confidence intervals and pvalue.