STAT 110: Assignment #9
Due Sunday, November 13th
Names:
1 – Wingspan and Height Comparisons with Gender
Tuesday in class we collected data on the heights and “wingspan” of the individuals in class. When analyzed data in class we found that there the mean wingspan was statistically significantly longer than the mean height when both were measured on the same person. In this analysis you will examine the same question, but do so separately for each gender. Data file: Height and Wingspan.JMP
Research Question: Is there evidence that wingspan and height have a mean difference different from zero when measured on the same person?
Males
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 between the height and wingspan for the population of adult males. Interpret this interval. (3 pts.)
Females
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 the height and wingspan for the population of adult females. Interpret this interval. (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.)
1