Description
There are 4 biostatistic questions. You must show complete work to be considered for full credit. For each question, use the specified format: manually or SPSS or both. Compile work into a single Word or pdf document. Copy and paste on answer document only relevant SPSS output with the exact answer highlighted. Never submit direct SPSS output as answer to a question.
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BIOS5300: HOME WORK#4
SECTION A: Manual Computation
For exercises 6.2.1 and 6.2.3 construct 90, 95 and 99 percent confidence intervals for the population
mean, and state the practical and probabilistic interpretations of each. Indicate which interpretation you
think would be more appropriate to use when discussing confidence intervals with someone who has
not had a course in statistics, and state the reason for your choice. Explain why the three intervals you
construct are not of equal width. Indicate which of the three intervals you would prefer to use as an
estimate of the population mean, and state the reason for your choice.
1. Daniel 6.2.1.
We wish to estimate the average number of heartbeats per minute for a certain population. The
average number of heart beats per minute for a sample of 49 subjects was found to be 90.
Assume that these 49 patients constitute a random sample, and that the population is normally
distributed with a standard deviation of 10.
2. Daniel 6.2.3.
In a length of hospitalization study conducted by several cooperating hospitals, a random
sample of 64 peptic ulcer patients was drawn from a list of all [peptic ulcer patients ever
admitted to the participating hospitals and the length of hospitalization per admission was
determined for each. The mean length of hospitalization was found to be 8.25days. The
population standard deviation is known to be 3days.
3. Daniel 6.3.4.
The concern of a study by Beynnon et al. (A-4) were nine subjects with chronic anterior cruciate
ligament tears. One of the variables of interest was the laxity of the anteroposterior, where higher
values indicate more knee instability. The researchers found that among subjects with ACL-deficient
knees, the mean laxity value was 17.4mm with a standard deviation of 4.3mm.
a) what is the estimated standard error of the mean.?
b) Construct the 99 percent confidence interval for the mean of the population from which the 9
subjects may be presumed to be a random sample.
c) What is the precision of the estimate?
d) What assumptions are necessary for the confidence interval you constructed?
4. Daniel 6.5.1.
Luna et al. (A-14) studied patients who were mechanically ventilated in the intensive care unit
of six hospitals in Buenos Aires, Argentina. The researchers found that of 472 mechanically
ventilated patients, 63 had clinical evidence of ventilator-associated pneumonia (VAP). Construct a
95 percent confidence interval for the proportion of all mechanically ventilated patients at these
hospitals who may be expected to develop VAP.
Daniel 6.9.5.
A sample of 25 physically and mentally healthy males participated in a sleep experiment in
which the percentage of each participant’s total sleeping time spent in a certain stage of sleep
was recorded. The variance computed from the sample data was 2.25. Construct a 95%
confidence interval for and 2
SECTION B: Use SPSS
Download and open the breast cancer survival data from the course website (You can also find it on
blackboard under “DATASETS”). The dataset consists of a data on 1207 breast cancer patients. Assume
that these patients are random sample from the population of all breast cancer patients. Use SPSS to
answer the following.
(a) Estimate the mean pathologic tumor size for breast cancer patient by computing a 95%
confidence interval. What are the assumptions for the validity of this CI?
(b) Now, let’s compare the mean pathologic tumor size for the two groups of patients: those
with progesterone receptor status negative and those with progesterone receptor status
positive. Construct a side-by-side boxplot of pathologic tumor size for these two groups of
patients. Do you see any difference between the two groups (ignore the outliers denoted by
circles and crosses)? Explain. Calculate a 90% CI for the difference in mean pathologic tumor
sizes of these two groups of patients assuming (i) equal variances for the two groups, and (ii)
unequal variances for the two groups. Do you conclude that these two groups differ in terms
of the mean pathologic tumor sizes? State your reason.
Important Notes:
For each of the above SPSS questions, (i) attach the SPSS output with relevant numbers
highlighted or circled and (ii) write your answer (including the reported CI’s) separately on piece
of paper. There is no need to calculate CI by hand, just report the CI you obtained from SPSS.
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