For each problemrequiring SAS include the appropriate SAS output as part of your answers and then create an appendix in which you will include the SAS commands.Do not print out the appendix; only submit it electronically.
Problem 1
It is reported that offspring of users of a certainrecreational drug may have a higher incidence of birth defectsthan the general population. To obtain information about apossible relationship between this drug and birth defects, 100offspring of female rats fed the drug and 100 offspring fromuntreated female rats are examined. From the experiment, we findthat 30% of the offspring of the treated rats have birth defects,and 20% of the offspring from untreated rats have birth defects.
(a) Construct using SAS a table that could be used to represent the information collected during this experiment and write an appropriate capture (i.e. brief description) for it.
(b) Can we conclude that the use of this recreational drug has an effect on the proportion of birth defects in their offspring? Conduct in SAS the appropriate test of hypotheses (include the appropriate output) and report the hypotheses tested, the corresponding test statistic and p-value and the decision and conclusion in the context of the study.
(c) Calculate the odds of bird defects in the two groups and the corresponding odds ratio. Interpret the OR in the context of the study. Obtain from SAS a 95% confidence interval for the OR and conduct an appropriate test of hypothesis of a drug effect based on this interval.
Problem 2
Assume that the Altigauge Manufacturing Company makes 80% of all electrocardiograph machines and the Cardioid Company makes the remaining 20%. Among the electrocardiograph machines made by Altigauge, 4% are defective. Among the Cardioid machines, 93% are not defective.
(a) Compute the probability that a randomly selected electrocardiograph machine is made by the Cardioid Company and it is not defective.
(b) Compute the probability that a randomly selected electrocardiograph machine is not defective.
(c) Compute the probability that the machine was made by the Altigauge Manufacturing Company given that it is not defective.
Problem 3
The data contained in the file Hospital (in the Final Take-Home Exam folder on BlackBoard) are a sample from a larger data set collected on people discharged from a selected Pennsylvania hospital as part of a retrospective chart review of antibiotic usage in hospitals. The variables recorded are:
|
Id
|
ID no.
|
|
Dur_stay
|
Duration of hospital stay
|
|
Age
|
Age
|
|
Sex
|
Sex (1=Male, 2=Female)
|
|
Temp
|
First body temperature following admission
|
|
WBC
|
First WBC (x103) following admission
|
|
Antibio
|
Received antibiotic (1=Yes, 2= No)
|
|
Bact_cul
|
Received bacterial culture (1=Yes, 2=No)
|
|
Service
|
Service (1=medical, 2=surgical)
|
(a) Construct an appropriate graphical summary for the variable WBC and compute the numerical summaries for it. Using the graph and the numerical summaries give a clear description of the distribution of this variable.
(b) Construct an appropriate graphical summary for the variable Service and interpret it.
(c) It is of interest to know if the WBC level is affected by whether or not a patient receives antibiotics. Use appropriate numerical and graphical summaries to investigate this matter and support your statement by using results from appropriate inferential methods. (Clearly justify your choice in terms of inferential method, in particular the decision to use either a parametric or a nonparametric method.)
(d) Can we conclude that there is a significant association between antibiotic use and bacterial culture? Conduct in SAS the appropriate test of hypotheses (include the appropriate output) and report the hypotheses tested, the corresponding test statistics and p-value, the decision and conclusion in the context of the study.
(e) Use the appropriate statistical methods (i.e. graphical summary, statistical model, etc.) to investigate how the age of the patient affects the duration of stay. Write a short report based on your analysis; include appropriate SAS output.
Problem 4
Three brands of tennis shoes are tested to see how many months of playing would wear out the soles. Eight pairs of brands A, N, and T are randomly assigned to a group of 24 volunteers. The following table shows the wear time, in months.
|
Brand A
|
Brand N
|
Brand T
|
|
8
|
4
|
12
|
|
10
|
7
|
8
|
|
9
|
5
|
10
|
|
11
|
5
|
10
|
|
10
|
6
|
11
|
|
10
|
7
|
9
|
|
8
|
6
|
9
|
|
12
|
4
|
12
|
(a) Using SAS conduct the ANOVA test. Is it appropriate to use the ANOVA test for this data? Do we have sufficient evidence to conclude that at least two of those treatments differ? (Define the parameter(s), state the hypotheses, obtain the value of the test statistic and the p-value, and state your conclusion in the context of the problem).
(b) If appropriate, use a multiple comparison procedures to identify which of the brands differ and interpret the information contained in the output.
(c) Conduct an appropriate nonparametric test for this data and discuss the results.
Problem 5
The following data pertain to the serum calcium measurements in units IU/L for 2 breeds of pigs, Chester White and Hampshire:
|
|
Serum Calcium Measurements
|
|
Chester White
|
116
|
112
|
82
|
63
|
117
|
69
|
79
|
97
|
71
|
88
|
104
|
87
|
|
Hampshire
|
62
|
59
|
80
|
105
|
60
|
71
|
103
|
79
|
89
|
87
|
93
|
100
|
(a) Using SAS obtain a 95% confidence interval for the difference in true mean serum calcium and interpret it in the context of the problem.
(b) Is there sufficient evidence in the data to conclude that Chester White has a significantly higher serum calcium then Hampshire?
• Identify the appropriate test of hypothesis for these data and clearly justify your choice (using graphical and numerical summaries);
• Define the parameter(s), statethe hypotheses, obtain the value of the test statistic and the p-value, and state your conclusion in the context of the problem).
(c) Based on your conclusion in part (b), which type of error (Type I or Type II) couldyou have made? Explain clearly the reasoning behind your answer.
Problem 6
Answer the following questions pertaining the paper Nosocomial Infection in Surgery Wards: A Controlled Study of Increased Duration of Hospital Stays and Direct Cost of Hospitalization, by Vegas et al.
(a) What was the purpose/objective of this study?
(b) What is the study design? Some potential characteristics of a study design are listed here, but please note, this list is not all-inclusive (Prospective/retrospective/cross-sectionalobservational study, Clinical trial, Randomized, Uncontrolled, Controlled, Blinded/open label, Multicenter, Active comparator, Placebo controlled, Cross-over).
(c) What is the population of interest in this study?
(d) What is the sample used in the study and what type of sampling design was used to obtain it?
(e) What are the main variables analyzed in this study? For each variable specify the type (i.e. qualitative, quantitative),the scale of measurement (i.e. nominal, ordinal, interval, ratio) and the role (i.e. response, explanatory, lurking). Specify thestatistical methods (descriptive and inferential) used for eachresponse variable (for example: matched-pair t test, Z confidence interval for proportions, χ2test, Mann-Whitney, etc.). Are these inferential methods appropriate (specify the assumptions for the method(s) and if they are met or not)? [Note: you can present all of the information using a table]
(f) What are the strengths and limitations/threats of this study? Comment on the internal and external validity of this study.
(g) Identify in Table 2 the two test results concerning the comparison between Matched infected and Rest of infected with respect to
Peripheral Line and Bladder Catheter. For each test result, specify the parameter(s) of interest, the null and alternative hypotheses, the significance level α (if given), the corresponding p-value and the decision (if α given) and conclusion reached based on the test.
(h) Identify in Table 6 the test result for Any localization. For this test result, specify the parameter(s) of interest, the null and alternative hypotheses, the significance level α (if given), the corresponding p-value and the decision (if α was given) and conclusion reached based on the test.
(i) Using the information given in the Discussion section, construct a 95% confidence interval for the difference in true proportion receiving antibiotics, infected patients before NI - uninfected patients. Interpret the interval in the context of the study.
(j) If you were the reviewer for this paper, what appropriate changes would you advice the authors to make in Tables 2 and 3 concerning the numerical summaries reported and the inferential methods used?
(k) Using SAS produce an appropriate graphical summary presenting the information given in Table 4.
Attachment:- Attechment.rar