Stat 301
Homework 2 answers
Fall 2015
1. Failure of electronic equipment
a) 1.935
b) 1.94
Note: why? se=0.131, so se/3 = 0.044. You report to the 100’ths place
c) 1.9
Note: why? I give you the sd, you need the se = 4.25/sqrt(50) = 0.60, se/3 = 0.2. You report to 10’ths
2. Heart rate during laughter
Yes, strong evidence that the heartrate during laughter exceeds 71 (two-sided p = 0.0002)
Note: No points off if you reported the one-sided p-value (< 0.0001) because the book’s question is onesided. The book’s question illustrates exactly why I always use two-sided tests. The physiology that is
described (reduced muscle tension and increased oxygenation) suggests that laughter should reduce the
heart rate. If the direction of the one-sided alternative (i.e. exceeds 71) was chosen because the sample
average was larger than 71, the analysis has been fudged.
3. Spidermite egg production
a) (21.1, 24.7)
Note: there is no version of Kelley’s rule for the CI endpoints (what is the se of an endpoint?). I use
common sense. If the interval is narrow, report more digits. If it is wide, report fewer.
b) (20.7, 25.1)
c) The 95% confidence interval is wider than the 90% interval. This is to be expected. A 95% interval is
more likely to include the true mean, so it has to be larger.
d) Somewhere between 5% and 10%. It is less than 10% because the 90% interval does not include 21
and more than 5% because the 95% interval does.
4. Decay of indoor air particles from cooking
a) The 95% confidence interval is (0.83, 1.36). We are 95% confident that the interval (0.83, 1.36)
includes the true population mean.
Note: Many other ways to word this.
b) If we repeated the study many times and constructed a confidence interval from each data set, 95%
of those confidence intervals would include the true population mean.
c) The population of decay rates is normally distributed.
5. Use of herbal medicines
a) eu is the patient. Patients are randomly sampled
b) The response variable is whether or not they used herbal medicines prior to surgery
c) ou is the patient. Because each patient is one row of data.
d) No problem because patients are randomly sampled
e) No problem because observations can be treated as independent; the ou is the same as the eu.
Note for most parts of 5 and 6: Giving us the number of eu’s or number of ou’s doesn’t answer the
question (what is the XX?). However, thinking about the number can be helpful because if the numbers
don’t match, the eu and ou can’t be the same.
6. Use of herbal medicines (version 2).
a) The eu is still the patient. Patients are randomly sampled
b) The ou is each surgery because there is one row of data for each surgery.
Note: Saying “the response” isn’t really enough because that answer is equally sort-of-correct for
problem 5. But there is a problem in 6) that isn’t in 5).
c) Yes, because the eu is not the same as the ou.
Note: Observations made on the same patient are likely to be similar. This violates independence.