Methods for the Life and Health Science
|Department of Statistics
Instructor: Ivo Dinov
|Due Date: Friday, Nov. 30, 2007
- (HW_7) Do these problems on pages
264-305 of Samuels & Witmer's text Statistics for the Life
Sciences, Prentice Hall (2003).
- 7.51: A study was
undertaken to compare the respiratory responses of hypnotized and
nonhypnotized subjects to certain instructions. The 16 male volunteers
were allocated at random to an experimental group to be hypnotized or
to a control group. Baseline measurements were taken at the start of
the experiment. In analyzing
the data, the researchers noticed that the baseline breathing patterns
of the two groups were different; this was surprising, since all the
subjects had been treated the same up to that time. One explanation
proposed for this unexpected difference was that the experimental group
were more excited in anticipation of the experience of
being hypnotized. The accompanying table presents a summary of the
baseline measurements of total ventilation (liters of air per minute
per square meter of body area).
- Use a T test to test a hypothesis of no difference against a
non-directional alternative (a=0.05).
- Use a T test to test a hypothesis of no difference against
the alternative that the experimental condition produces a larger mean (a=0.05).
- Which of the two tests is more appropriate? How are the
results different? Interpret and explain!
- 7.52: In a study of
lettuce growth, 10 seedlings were randomly
allocated to be grown in either standard nutrient solution or in a
containing extra nitrogen. After 22 days
of growth, the plants were harvested and weighed, with the results
given in the
table. Are the data sufficient to
conclude that the extra nitrogen enhances plant growth under these
conditions? Use a t test at a = 0.10
directional alternative. (Assume that
the data are normally distributed.) Does extra nitrogen enhance lettuce
- 7.59: There is an old
folk belief that the sex of a baby can be guessed before birth on the
basis of its heart rate. In an investigation to test this belief, fetal
heart rates were observed for mothers admitting to a maternity ward.
The results are summarized below.
- Construct a 95% CI(difference of the population means). Does
the confidence interval support the claim? Explain the results in the
context of the observations.
- 7.66: Suppose you are
planning a greenhouse experiment on growth of pepper plants. You will
grow n individually potted seedlings in standard soil and another n
seedlings in a specially treated soil. After 21 days you will measure Y
= total stem length (cm) for each plant. If the effect of the soil
treatment is to increase the population length mean stem length by 2
cm, you would like to have a 90% chance of rejecting Ho with
one-tailed T test. Data from a pilot study on 15 plants grown in
standard soil gave the following y- = 12.5 and S = 0.8 cm.
- Suppose you want to test at a = 0.05. Use the pilot
information to determine what n you should use.
- What conditions are required for the validity of the
calculations in part 1?
- Suppose you test at a more conservative value of a=0.01. What
value of n should you use? Explain.
- 7.79: A researcher
measured the concentration of the neurotransmitter dopamine in 6 rats
exposed to toluene and six control rats. The concentrations of dopamine
in the striatum of the two populations are included in the table.
- Use Wilcoxon-Mann-Whitney test to compare the treatments at
a=0.05, against a non-directional alternative
- Use Wilcoxon-Mann-Whitney test to compare the treatments at
a=0.05, against an alternative that toluene increases dopamine
concentrations in the striatum.
- 7.84: Human
beta-endorphin (HBE) is a hormone secreted by the pituitary gland under
conditions of stress. An exercise physiologist measured the resting
(unstressed) blood concentration of HBE in two groups of men: Group 1
consisted of 11 men who had been jogging regularly for some time, and
group 2 consisted of 15 men who had just entered a physical fitness
program. (This data was from
the same research study on HBE we used in your Inference for the
Population Mean HW, exercise 6.16.) The results are given in the
following table. Use the Wilcoxon-Mann-Whitney test to compare the two
|39 40 32 60
|70 47 54 27 31
|19 52 41 32
|| 42 37 41 9 18
|13 37 28
|33 23 49 41 59
- 7.90: A plant
physiologist conducted an experiment to determine whether mechanical
stress can retard the growth of soybean plants. Young plants were
randomly allocated to two groups of 13 plants each. Plants in one
group were mechanically agitated by shaking for 20 minutes twice daily,
while plants in the other group were not agitated. After 16 days
of growth, the total stem length (cm) of each plant was measured.
- Use a T test to compare the treatments at a = 0.01, let the
alternative hypothesis be that stress retards growth.
- Explain and interpret your findings.
- 7.99: In an
investigation of the possible influence of dietary chromium on diabetic
symptoms, 14 randomly selected rats were fed a low-chromium diet and 10
were fed a normal diet. One response was the activity of the liver
enzyme GITH, which was measured using a radioactively labeled molecule.
The accompanying table shows the results, expressed as thousands of
counts per minute per gram of liver.
- Are these observational data or do the data come from a
- Use SOCR
Charts to plot the data and comment on whether there appears to
be any difference in GITH activity between the diets. Comment on the
symmetry of the data, whether there are any outliers, and whether the
variances appear to be similar.
- Is there evidence that mean GITH activity is
different for the two diets? (State null and alternative hypotheses and
base your conclusion on the p-value).
- Calculate the 95% confidence interval for the mean
difference in GITH activity.
- 7.103: In a study
of the effect of amphetamine on water consumption, a pharmacologist
injected four rats with amphetamine and four with saline as
controls. She measured the amount of water each rat consumed in
24 hours; the following are the results, expressed as ml water per kg
- Use a t-test to compare the treatments at alpha = .05. Let
alternative hypothesis be that amphetamine tends to suppress water
consumption. Write down the null and alternative hypotheses, test
statistic, P-value and decision.
- Use a Wilcoxon-Mann-Whitney test to compare the treatments at
alpha = .05, with the directional alternative that amphetamine tends to
suppress water consumption