STAT 110: Assignment #10
Due Sunday, December 2nd
Names:
1 – Helium Football
Two identical footballs, one air-filled and one helium-filled, were used outdoors on a windless day, at Ohio State’s sports complex, so that wind would not be a factor in the ball’s flight path. This was a blind study; meaning the novice kicker did not know which football was filled with helium and which was filled was air. Each football was kicked 39 times. The kicker randomly switched footballs after each kick. This was done to minimize the effects of confounding variables such as his leg getting tired or improved kicks with practice. The distance from the place of the kick to where the ball eventually landed was carefully measured. The data collected are in the file Helium-football.JMP.
FYI: This was also the subject of a Mythbusters® episode 47 (2006).
Research Question: Is there evidence that the helium filled football goes further than the non-helium filled ball?
a)State Ho and Ha in words and in terms of the mean difference ((3 pts.)
b) Check assumptions required for using a t-test, do they appear to be satisfied for these data? (2 pts.)
c)Conduct a test that allows you answer the research question and state your conclusion. (3 pts.)
d)Construct a 95% CI for the mean difference in distance traveled for helium-filled footballs vs. those filled with air. Interpret this interval. (3 pts.)
e)Select Graph > Overlay Plot and put both Air and Helium in the Y-box and Trial in the X-box. Then select Connect Through Missing from the pull-down menu above the plot. Does it appear the kickers distances changed over time? Do the conclusions of the t-test seem reasonable given what you see in this plot? (3 pts.)
2 – Treatment of Patients with Anorexia Nervosa
The data in the file Anorexia-bodymass.JMPcontain the results from a study of n = 20 patients admitted to a hospital for treatment of anorexia nervosa. At the time of admission the body mass index (BMI) of each patient was taken. Also a minimal preferred BMI was determined for each patient at the time of admission based upon their height. At the time of discharge from the hospital each patients BMI was measured as well. There are two main research questions of interest to the researchers.
Research Question 1: Is there evidence that mean BMI increases for patients during the course of treatment at the hospital, if so, how much does it increase by on average?
Research Question 2: Is there evidence that mean BMI at discharge is different from the minimal preferred BMI for the patients? In other words, on average are patients meeting the BMI goal at the time of discharge?
Research Question 1
a)State Ho and Ha in words and in terms of the mean difference ((3 pts.)
b) Check assumptions required for using a t-test, do they appear to be satisfied for these data? (2 pts.)
c)Conduct a test that allows you answer the research question and state your conclusion. (3 pts.)
d)Construct a 95% CI for the mean BMI gain for the patients. Interpret this interval. (3 pts.)
Research Question 2
e)State Ho and Ha in words and in terms of the mean difference ((3 pts.)
f) Check assumptions required for using a t-test, do they appear to be satisfied for these data? (2 pts.)
g)Conduct a test that allows you answer the research question and state your conclusion. (3 pts.)
h)Construct a 95% CI for the mean difference between discharge BMI and preferred BMI. Interpret this interval. (3 pts.)
3 – Middle Ear Effusion Times and Breast vs. Bottle-Fed Infants
A common symptom of otitus media in young children in the prolonged presence of fluid in the middle ear, known a middle-ear effusion. The presence of fluid may result in termporary hearing loss and interfere with normal learning skills in the first two years of life. One hypothesis is that babies who are breast-fed for at least 1 month build up some immunity against the effects of the disease and have less prolonged effusion than do bottle-fed babies. A small study of 24 pairs of babies is set up, where the babies are matched on a one-to-one basis according to age, sex, socioeconomic status, and type of medications taken. One member of the matched pair is a breast-fed baby, and other member is a bottle fed baby. The outcome variable is the duration of middle-ear effusion after the first episode of otitus media. The results are shown below.
in bottle-fed baby / Difference
d =
1 / 20 / 18
2 / 11 / 35
3 / 3 / 7
4 / 24 / 182
5 / 7 / 6
6 / 28 / 33
7 / 58 / 223
8 / 39 / 57
9 / 17 / 76
10 / 17 / 186
11 / 12 / 29
12 / 52 / 39
13 / 14 / 15
14 / 12 / 21
15 / 30 / 28
16 / 7 / 8
17 / 15 / 27
18 / 65 / 77
19 / 10 / 12
20 / 7 / 8
21 / 19 / 16
22 / 34 / 28
23 / 25 / 20
Research Question: Do these data provide evidence that breast-fed babies have shorter durations of effusion when compared to bottle-fed babies that are the same age, sex, socioeconomic status, and on the same medications? These data are in the file Ear Effusion.JMP.
a) Why are we treating these samples as dependent? (1 pt.)
b)Do you think matching these infants on the basis of age, sex, socioeconomic status, and medications taken, is valid? Can you think of other factors that could be used for matching? (2 pts.)
c)What test procedure do you think should be used for analyzing these data? Explain
your choice, conduct the analysis, and summarize your findings. (5 pts.)
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