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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.

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.

5. 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}

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.

- 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?
- 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-sideboxplot 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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