Practice Questions
October 4, 2015
1. (This problem refers to the data in Chap 9. Q11)
When eight persons in Massachusetts experienced an unexplained episode
of vitamin D intoxication that required hospitalization, it was suggested
that these unusual occurrences might be the result of excessive supplementation of dairy milk. Blood levels of calcium and albumin for each
individual at the time of hospital admission are shown below.
Calcium
(mmol/l)
2.92
3.84
2.37
2.99
2.67
3.17
3.74
3.44
Albumin
(g/l)
43
42
42
40
42
38
34
42
Table 1: Data of question 1.
Read all parts before you start answering. Assume that calcium levels
for people in Massachusetts who experience vitamin D intoxication are
normally distributed.
(a) Obtain a 95% confidence interval for the mean calcium level for people in this population and interpret the meaning behind 95% confidence.
(b) For healthy individuals a normal calcium level can be as high as 2.58
mmol/L. One claims that the mean calcium level for Massachusetts
inhabitants who experience vitamin D intoxication is above that.
Test this claim with a level of significance of 0.01. Write down clearly
the steps using the p-value approach.
(c) If the value µ0 in the null hypothesis is changed to 2.7 and we are now
conducting a test at a 0.05 level of significance and the test becomes
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now two-tailed. Can you quickly determine whether we need to reject
H0 or not without doing any additional calculations? Explain.
2. (Chap 9. Q12) Serum zinc levels for 462 males between the ages of 15 and
17 are saved under the variable name zinc in the data set serzinc. The
units of measurement for serum zinc level are micrograms per deciliter.
(a) Plot the histogram of the serum zinc level.
(b) Find a two-sided 95% confidence interval for µ, the true mean serum
zinc level for this population of males.
(c) Interpret this confidence interval.
(d) Calculate a 90% confidence interval for µ.
(e) How does the 90% confidence interval compare to the 95% interval?
3. (Chap 10. Q16)
The Bayley Scales of Infant Development yield scores on two indices–
the Psychomotor Development Index (PDI) and the Mental Development
Index (MDI)–which can be used to assess a child’s level of functioning
in each of these areas at approximately one year of age. Among normal
healthy infants, both indices have a mean value of 100. As part of a
study assessing the development and neurologic status of children who
have undergone reparative heart surgery during the first three months
of life, the Bayley Scales were administered to a sample of one-year-old
infants born with congenital heart disease. The data are contained in the
data set heart; PDI scores are saved under the variable name pdi, while
MDI scores are saved under mdi.
(a) At the 0.05 level of significance, test the null hypothesis that the
mean PDI score for children born with congenital heart disease who
undergo reparative heart surgery during the first three months of life
is equal to 100, the mean score for healthy children. Use a two-sided
test. What is the p-value? What do you conclude?
(b) Conduct the analogous test of hypothesis for the mean MDI score.
What do you conclude?
(c) Construct 95% confidence intervals for the true mean PDI score and
the true mean MDI score for this population of children with congenital heart disease. Does either of these intervals contain the value
100? Would you have expected that they would?
Note: There was some ambiguity here about whether the question was
asking us to analyze all n = 143 babies, or to restrict analyses to the
subset of n = 70 babies with “trtment” equal to 1. We assume that the
question was asking us to analyze all n = 143 babies.
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