Complete the following:
1. A group of 25 subjects have their diastolic blood pressures measured. The results, in SPSS are:
|-----------|-------|--------|
|N |Valid |25 |
|-------|--------|
| |Missing|0 |
|-----------|-------|--------|
|Median |85.00 |
|-------------------|--------|
|Mode |82.00 |
|-------------------|--------|
|Minimum |55.00 |
|-------------------|--------|
|Maximum |110.00 |
|-----------|-------|--------|
|Percentiles|25 |71.00 |
| |-------|--------|
| |50 |85.00 |
| |-------|--------|
| |75 |98.00 |
|--------|-------|--------|
Don't worry about values exactly at the endpoints of these intervals. Do the calculations roughly.
a. What percentage of subjects were from 55 to 85?
b. What percentage of subjects were < 85?
c. What percentage of subjects were from 71 to 85?
d. What percentage of subjects were > 71?
e. What percentage of subjects were > 98?
f. Is there one value more common than the rest, and if so, what is it?
2. Assume you have already been give a Z value. This saves you a step. Consider and determine the following probabilities
A. Pr (-1 < Z < 1)
B. Pr (0 < Z < 1)
C. Pr (Z > 1)
D. Pr (-1 < Z < 0)
E. Pr (Z < -1)
F. Pr (Z > -2)
G. Pr (-1 < Z < 2)
3. Suppose the mean systolic blood pressure in a group of individuals is 150 mmHg, with a standard deviation of 15. Assuming SBP follows a normal distribution in this population, compute
A. Pr (135 < value < 165)
B. Pr (value > 165)
C. Pr (value < 135)
D. Pr (138.75 < value < 161.25)
4 Compute the 5th, 50th, and 95th percentiles of SBP from the previous question.
In questions 5 - 7, use the 1 and 2 SD rules, without the table.
5.In general, what percentage of a Gaussian data set is within 1 SD of the mean? What percentage is within 2 SD's of the mean?
6.If the mean grade on an exam was 80, SD = 6, where did about 68% of the grades fall? How about 95%? Assume the grades are Gaussian.
7.Consider the following data: 1, 1, 2, 2, 4, 5, 6, 9, 40, 200
Use the 68% and 95% rules to test the normality of these data.
8.A researcher studying a subtype of lymphocytes obtains a sample mean of 100 per mL, and a standard deviation of 20, with 25 subjects. Within what interval can you be roughly 68% sure the population mean number of these cells per mL lies? How about 95% sure?
9.A researcher has a sample of 500 subjects. The mean is 40, median is 20, range 10-100.
a.Could this researcher calculate a useful interval with 95% probability of containing the population mean (using the mean and SEM)? Explain
b.Could the researcher use the mean and SD to usefully estimate where 95% of the individual subject values were? Explain
c.If there were 10 subjects, would your answers to a and b change?