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 5
Due Date: Wednesday, Nov. 14, 2007
Turn in your papers in class, before class starts

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_5) Do these problems on pages 185-218, Samuels & Witmer's text Statistics for the Life Sciences, Prentice Hall (2003)
• 6.4A zoologist measured tail length in 86 individuals, all in the one-year age group, of the deermouse Peromyscus.  The mean length was 60.43 mm and the standard deviation was 3.06 mm. This table represents the frequency distribution of the data:
• Calculate the standard error of the mean.
• Construct a Histogram of the data using SOCR Charts. Let y-, SD and SE denote the sample average, sample standard deviation and standard error of the mean. Mark the intervals y- +/- SD and y- +/- SE.
 Tail Length Number of Deermice 52-53 1 54-55 3 56-57 11 58-59 18 60-61 21 62-63 20 64-65 9 66-67 2 68-69 1 Total 86

• 6.12: Six healthy three-year-old female Suffolk sheep were injected with the antibiotic Gentamicin at a dosage of 10 mg/kg body weight. Their blood serum concentrations (μg/mLi) of Gentamicin 1.5 hours after injection were as follows: 33  26   34   31   23   25. For these data, the mean is 28.7 and the standard deviation is 4.6.
• Construct a 95% confidence interval for the population mean
• Define in words the population mean that you estimated above. (See Example 6.1 in the textbook.)
• Is it typical for the 95% confidence interval constructed in the first part to nearly contain all of the observations?
• 6.16: Human beta-endorphin (HBE) is a hormone secreted by the pituitary gland under conditions of stress. A researcher conducted a study to investigate whether a program of regular exercise might affect the resting (unstressed) concentration of HBE in the blood. He measured blood HBE levels, in January and again in May, in ten participants in a physical fitness program. The results were as shown in the table.
 HBE Level (pg/mLi) Participant January May Difference 1 42 22 20 2 47 29 18 3 37 9 28 4 9 9 0 5 33 26 7 6 70 36 34 7 54 38 16 8 27 32 -5 9 41 33 8 10 18 14 4 Mean 37.8 24.8 13.0 SD 17.6 10.9 12.4
• Conduct a 95% confidence interval for the population mean difference in HBE levels between January (unstressed level) and May (HBE level possibly perturbed by exercise). (Hint: You need to use only the values in the right-hand column and your Ho will be μ=0.)
• Interpret the confidence interval from the first part - that is explain what the confidence interval tells you about the HBE levels (see examples 6.9 and 6.10 in the textbook.)
• 6.41: Researchers tested patients with cardiac pacemakers to see if use of cellular telephone interferes with the operation of the pacemaker. There were 959 tests conducted for one type of cellular telephone; interference with pacemakers (detected electrocardiographically) was found in 15.7% of these tests:
• Use these data to construct an approximate 90% confidence interval.
• Interpret the interval in the first part in the context of the data.
• 6.52: The diameter of the stem of a wheat plant is an important trait because of its relationship to breakage of the stem, which interferes with harvesting the crop.  An agronomist measured stem diameter in 8 plants of the Tetrastichon cultivar of soft red winter wheat.  All observations were made three weeks after flowering of the plant.  The stem diameters (mm) were as follows: 2.3  2.6  2.4  2.2  2.3  2.5  1.9  2.0. And the mean of these data is 2.275 and the standard deviation is 0.238.
• Calculate the SE of the mean
• Construct a 98% confidence interval for the population mean.
• Interpret your confidence interval in the context of this setting.  That is, what do the numbers in the confidence interval mean?
• Suppose that the data on these nine plants are regarded as a pilot study, and that the agronomist now wishes to design a new study for which she wants the margin of error to be only half as large as was calculated earlier.  How many plants should be measured in the new study?
• 6.64: An agronomist selected six wheat plants at random from a plot and then for each plant chose 12 seeds from the main portion of the wheat head. By weighting, drying and reweighting, she determined the percent of moisture in each batch of seeds. The results were as follows: 62.7, 63.6, 60.9, 63.0, 62.7, 63.7.
• Calculate the mean, standard deviation and the standard error of the mean.
• Construct a 90% confidence interval for the mean.
• 6.69: At a certain university there are 25,000 students. Suppose you want to estimate the proportion of those students that are nearsighted. The prevalence of nearsightedness in the general population is 45%. using this as a preliminary guess of the student proportion, p, how many students would you need to randomly sample if you want the standard error of your estimate to be <= 2 percentage points?

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