Biometry Assignment # 6 (49 pts.)
Introduction to Hypothesis Testing - (one and two population inference)
A few of these problems require entering data into JMP. If you have any questions regarding this process please ask me in class or come see me in my office. Refer to the first JMP tutorial for some general help with data entry.
For all problems be sure to do the following:
- check required assumptions and take appropriate actions
- state the null and alternative hypotheses
- report the p-value and your decision
- state conclusion in words - (e.g. There is sufficient evidence (p = .0013) to indicate that the mean hemoglobin level for non-cadmium exposed dogs exceeds that of dogs who have been exposed to cadmium.)
1 –Maine Mercury Study
Data File: Maine Mercury Study
The U.S. Food and Drug Administration has determined that samples with more than 1.0 ppm mercury are above the safety limit. Maine uses .43 ppm, to be high enough to consider taking action (e.g., issuing a health advisory, considering methods of clean-up, etc.). As indicated by the data collected here, are mercury levels high enough to be of concern in Maine? To answer this question determine whether the “average” mercury level found in fish in Maine lakes exceeds the .43 ppm cutoff. Summarize your findings. (Hint: Given that Hg levels are considerably right skewed you might consider looking at the Hg levels in the log scale) (5 pts.)
2 - Prostate-Specific Antigen (PSA) Levels and Cancer Diagnosis
Babaian et al. "The Role of Prostate-Specific Antigen as Part of the Diagnostic Triad and as a Guide When to Perform a Biopsy", Cancer, 68, (1991) state that prostate-specific antigen (PSA), found in the ductal epithelial cells of the prostate, is specific for prostatic tissue and is detectable in serum from men with normal prostates and men with either benign or malignant diseases of this gland. They determined the PSA values in sample of 124 men who underwent a prostate biopsy. Sixty-seven of the men had elevated PSA values (> 4 ng/ml). Of these, 46 were diagnosed as having cancer. Ten of the 57 men with PSA values 4 ng/ml had cancer. On the basis of these data may we conclude that, in general, men with elevated PSA values are more likely to have prostate cancer? Let = .01.
Use both the standard normal test statistic and Fisher's Exact Test to test the hypothesis of interest. To perform Fisher's Exact Test you will need to enter the data in JMP. You will need three columns (two with data type = character) to enter these data. The first column should contain information about their PSA level (high or low) and the second column should contain the results of their cancer diagnosis (yes or no). The last column (Freq) should specify the appropriate cell frequencies. Make sure that the numbers in this column are interpreted as frequencies by right-clicking at the top of the column and select Freq from the Preselect Role pull out menu.
a) Standard normal test, be sure to show your work! (4 pts.)
b) Fisher's Exact Test (2 pts.)
c) Find CI’s for both the RR and OR for cancer associated with having an elevated PSA level. Discuss. (6 pts.)
3 -A Simple Genetics Experiment
In a genetics experiment, the Mendelian law is followed as expected if one-eighth of the offspring exhibit a certain recessive trait. Analysis of 500 randomly selected offspring indicates that 83 exhibited the recessive trait. Is the Mendelian law being followed as expected? Use .01 as the significance level of the test. Summarize your findings. (5 pts.)
4 - Preeclampsia and Gestational Age
The goal of study conducted by Baker et. al. was to determine whether medical deformation alters in vitro effects of plasma from patients with preeclampsia on endothelial cell function to produce a paradigm similar to in vivo disease state. Subjects were 24 nulliparous pregnant women before delivery, of whom 12 had preeclampsia and 12 were normal pregnant patients. Among the data collected were the gestational ages (in weeks) at delivery.
Is there evidence to suggest that the mean gestational age at delivery for mothers with preeclampsia is lower than that for mothers with a normal pregnancy? Use JMP to analyze these data. You can enter the data in JMP yourself. You will need two columns, one to denote the group and the other to contain the response, in this case gestational age at birth. Be sure to check assumptions and perform your analysis accordingly.
Data:
Preeclampsia: 38, 32, 42, 30, 38,35, 32, 38, 39, 29, 29, 32
Normal: 40, 41, 38, 40, 40, 39, 39, 41, 41, 40, 40, 40
a) Perform a hypothesis test answer the question of interest. Summarize your findings. (4 pts.)
b) Find a 95% CI for the difference in the population means. Discuss. (2 pts.)
5 -Middle Ear Effusion in Breast-Fed and 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 temporary 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.
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
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? Enter these data into JMP and conduct the appropriate analysis. (6 pts.)
6 - Risk Factors for Having a Child with Low Birth Weight
Data File:Lowbirth.JMP
The purpose of this study was to identify potential risk factors for low birth weight. To do this, a random sample of new mothers was taken from a BaltimoreHospital and the birth weight was recorded. Also the following categorical variables were measured: previous history of premature labor (Prev?), hypertensive during pregnancy (Hyper?), smoking status (Smoke?), uterine irritability during pregnancy (Uterine), and minority status (Minority). Use comparative methods to compare the actual birth weights across the levels of these factors. Be sure to check assumptions.
Research Question: Which factors have the largest birth weight differences?
Use both hypothesis tests and confidence intervals to answer the research question above.
You may want to use the following table to help organize your findings.
Risk Factor / Sample Mean
(Risk Factor Present) / Sample Mean
(Risk Factor Absent) / p-value / Confidence Interval for
Summarize your findings in a clearly written paragraph, citing p-values and confidence intervals as needed. (15 pts.)