Stat 301
HW 2
Due: 11 Sept / 14 Sept 2015
1. The data in panelfail.txt are the longevity (time from purchase to failure, in years) of a certain
type of electronic equipment. These can be treated as a random sample of all pieces of this
type of equipment sold in 2010.
(a) Estimate the mean longevity. Report the mean as given by JMP.
(b) Use Kelley’s rule to decide on the appropriate value to report.
(c) Imagine a new data set with different numbers; the sample average of the new data is
exactly the same as in part a, but the sample standard deviation of new data is 4.25.
Use Kelley’s rule to appropriately report the mean for these new data.
2. Text problem 1.58 (p. 50). The data are in heartrate.txt. Answer the book’s question by
reporting the p-value and writing a one-sentence conclusion.
3. Based on text problem 1.50 (p. 42). Ignore the book’s questions. The data for eggs produced
when the female is treated with antibiotic are in spidermite.txt.
(a) Calculate a 90% confidence interval for the population mean number of eggs produced
when only the female is treated with antibiotic.
(b) Calculate a 95% confidence interval for the population mean number of eggs produced
when only the female is treated with antibiotic.
(c) Which interval is wider? Briefly explain why this is to be expected (or, why this is a
surprising result).
(d) Based on their long-time experience, the Japanese researchers believe that the average
fecundity (# of eggs per female) is 21.0. Based on the confidence intervals you calculated
in parts a and b, what can you say about the two-sided p-value for the test of the null
hypothesis that mean fecundity when the female is treated with antibiotic equals 21?
Briefly explain your answer.
4. Text problem 1.46 (p. 41) The data are in DECAY.txt
5. Text problem 1.4 (p. 3). New questions:
(a) Identify the experimental unit for the study. Briefly explain your choice.
(b) Identify the variable measured for each experimental unit. (No explanation needed).
For the remaining parts, presume that this survey also asked how many different types of
herbal or alternative medicine they used. The answer is a number, e.g. 0, 1, 2, etc. You are
interested in estimating the mean number of herbal/alternative products that were used. The
population of interest is all patients at the hospitals in the study. Remember (from last week’s
HW), that the data are a random sample of patients at these hospitals.
(c) If there is one row of data per surgical patient, so 500 rows of data, what is the observational unit?
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(d) Based on your answers to the appropriate parts a-d, will there be a problem using the
sample average to estimate the population average? Briefly explain why or why not.
(e) Based on your answers to the appropriate
parts a-d, will there be a problem using the
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usual standard error formula (sd / 500) to describe the precision of the estimated
mean? Briefly explain why or why not.
6. New problem. Extension of question 5. Some of the 500 patients have had multiple surgeries.
Presume that the survey asks them to answer the “how many types of herbal/alternative
medicine” question for each surgery. Some patients provide one answer, some provide two
and a few provide three answers. There are a total of 720 rows of data. Each row corresponds
to one surgery.
(a) What is the experimental unit for this version of the survey? Briefly explain.
(b) What is the observational unit for this version of the survey? Briefly explain.
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(c) Will there be a problem using the usual standard error formula (sd / 720) to describe
the precision of the estimated mean? Briefly explain why or why not.
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