Ivo Dinov
UCLA Statistics, Neurology, LONI

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STAT 13

Introduction to Statistical Methods for the Life and Health Science

Department of Statistics

## Instructor: Ivo Dinov

Homework 7
Due Date: Friday, Nov. 30, 2007

Please, submit your homework right after lecture on the due date. See the HW submission rules. On the front page include the following header.
• (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!

 Experimental Control 1 5.32 4.50 2 5.60 4.78 3 5.74 4.79 4 6.06 4.86 5 6.32 5.41 6 6.34 5.70 7 6.79 6.08 8 7.18 6.21 n 8 8 y- 6.169 5.291 S .621 .652
• 7.52: In a study of lettuce growth, 10 seedlings were randomly allocated to be grown in either standard nutrient solution or in a solution 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 against a directional alternative.  (Assume that the data are normally distributed.) Does extra nitrogen enhance lettuce growth?
•  Nutrient Solution n Mean SD Standard 5 3.62 0.54 Extra nitrogen 5 4.17 0.67
• 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.

 Heart Rate (bpm) n Mean SE Males 250 137.21 0.62 Females 250 137.18 0.53
• 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.
 Dopamine(ng/g) Toluene Control 3420 1820 2314 1843 1911 1397 2464 1803 2781 2539 2803 1990
• 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 populations.
 Joggers Fitness Program Entrants 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.

 N Mean Std Dev SE Mean Control 13 30.59 2.13 0.59 Stress 13 27.78 1.73 0.48

• 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 designed experiment?
• 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.
 Low-Chromium Diet 42.3 51.5 53.7 48 56 55.7 54.8 52.8 51.3 58.5 55.4 38.3 54.1 52.1 Normal Diet 53.1 50.7 55.8 55.1 47.5 53.6 47.8 61.8 52.6 53.7
• 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 body weight.
• Use a t-test to compare the treatments at alpha = .05. Let the 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
 Amphetamine 118.4 124.4 144.3 105.3 Control 122.9 162.1 184.1 154.9

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