Stat 301 B -- Fall 2015 -- Midterm exam 1
1 October 2015
Questions
Instructions:
1. Please put your name on the back of the last page. I don’t want to see your name until I have
finished grading.
2. Background information for each problem is given in the second packet.
3. Read each question carefully and completely. Ask if you don’t understand something.
4. Answer each question and show work in the space provided. You may use the back of a page as
scratch paper, but I will only read and evaluate what you put in the answer spaces.
5. Use the JMP output wherever you can. I am very happy to answer questions along the lines of
‘(You pointing to a number on the JMP output) Is this the confidence interval for the regression
slope?’.
There are 100 points of questions.
Problem 1. Pace of life in US cities.
The first few questions concern the walk variable.
1. 3 pts. Are the 36 observations a sample or a population (in the statistical meaning of a
population)? Briefly explain your answer.
2. 3 pts. We have talked about two measures of location, the mean and the median. Do you
expect the values of the mean and median for the walk variable to be about the same value, or
not? Briefly explan your answer.
3. 3 pts. The average of the 36 walk values is 21.4. Is this number a statistic or a parameter?
Briefly explain your choice.
The last set of questions concern the talk variable.
4. 4 pts. Is the distribution of values symmetrical or not? Briefly explain your answer.
5. 3 pts. What is the median of these values?
6. 5 pts. JMP reports the mean as 20.5833333. Is this an appropriate way to report this number?
If not, what is an appropriate value to report. Briefly explain your answer(s).
7. 4 pts. Calculate the T statistic to test H0: population mean equals 22.0. Show your work.
8. 3 pts. If possible from the provided JMP output, report the two-tailed p-value for the test of the
null hypothesis that the mean equals 22.0 If not possible, say “not possible”.
Problem 2. Music and attention span.
9. 4 pts. Calculate the pooled standard deviation. Show your work.
10. 5 pts. (Put your answer on the top of the next page) Compare the number you calculated in
part 9 to the sd for the Music group and the sd for the Control group. Is the sd from part 9:
a. larger than both the Music sd and the Control sd,
b. in between the sd’s for the two groups, or
c. smaller than both the Music sd and the Control sd?
Briefly explain your choice. For example, if you answered a) larger, then you should explain why
it is reasonable that the pooled sd is larger than both the Music sd and the Control sd.
Note: the numbers you need for the individual groups (Music or Control) are in the JMP output.
11. 4 pts. Calculate the degrees of freedom (df) for the pooled standard deviation. Show your work.
12. 5 pts. Compare the number you calculated in part 11 to the df for the Music group and the df
for the Control group. Is the df from part 11:
a. larger than both the Music df and the Control df,
b. in between the df’s for the two groups, or
c. smaller than both the Music df and the Control df?
Briefly explain your choice (i.e., why this should be expected, as in question 10)
13. 4 pts. Is it appropriate to assume equal variances for these data? Briefly explain why or why
not.
14. 4 pts. Calculate the standard error of the difference between the Music and Control group
means, assuming equal variances. Show your work.
15. 5 pts. Compare the number you calculated in part 14 to the se for the mean of the Music group
and the se for the mean of the Control group? Is the se from part 14:
a. larger than both the Music se and the Control se,
b. in between the se’s for the two groups, or
c. smaller than both the Music se and the Control se.
Briefly explain your choice (as in questions 10 and 12).
16. 3 pts. What is the two-sided p-value for the test of the null hypothesis that the mean attention
span in the Music group is the same as that for the Control group?
17. 3 pts. Write a one-sentence conclusion about the results of the hypothesis test in question 16.
18. 4 pts. Will 0 be inside or outside the 99% confidence interval for the difference between the
two means? Briefly explain your answer.
Problem 3: patch area and butterfly species diversity
19. 4 pts. What variable is the independent variable in this regression?
What variable is the dependent variable in this regression?
20. 3 pts. What is the estimated slope of the regression line?
21. 3 pts. What are the units for the regression slope.
Note: The units for species are “number of species”. The units for logArea are “logArea”
22. 5 pts. It is appropriate to conclude from this analysis that “Increasing the area of a patch
increases the average number of butterfly species”? Briefly explain why or why not.
23. 5 pts. Briefly explain what the estimated intercept, 36.25, “means” in the context of this study.
24. 3 pts. Predict the average number of butterfly species that would be found if a patch had a log
Area of 1.5. Show your work.
25. 4 pts. The standard error for the predicted number of species (In the JMP output) is smaller for
patches of 1 log Area (Area of 10 ha) than it is for patches of 3 log Area (Area of 1000 ha).
Briefly explain why this is to be expected.
26. 3 pts. The mean predicted number of species for patches of 250 ha is 104.59 species (see JMP
packet). Report the 95% interval that appropriately describes the uncertainty in this estimate.