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biostatistics

Questions and Answers of Biostatistics

Suppose you are planning another experiment like the one in Exercise 9.20.Based on that data: (1) you are willing to assume that the standard deviation of the difference in means is 1.5°F, and (2)
Consider the paired t test that was used with the data in Table 9.1, what would the power of the test be if the alternative is that the mean temperature differs by 3 degrees between the cities? What
Find the critical values for t that correspond to the following:a. n = 12, = 0.05 one-tailed (right)b. n = 12, = 0.01 one-tailed (right)c. n = 19, = 0.05 one-tailed (left)d. n = 19, = 0.05
Find the area under the t-distribution between zero and the following values:a. 2.62 with 14 degrees of freedomb. –2.85 with 20 degrees of freedomc. 3.36 with 8 degrees of freedomd. 2.04 with 30
Recent advances in DNA testing have helped to confirm guilt or innocence in many well-publicized criminal cases. Let us consider the DNA test results to be the gold standard of guilt or innocence and
Redo Exercise 9.14 but use a one-tailed (left-tail) test.
Describe the differences between a one-tailed and a two-tailed test. Give examples of when it would be appropriate to use a two-tailed test and when it would be appropriate to use a one-tailed test.
Test the hypothesis that a normally distributed population has a mean blood glucose level of 100 (2 = 100). Suppose we select a random sample of 30 individuals from this population (X = 98.1, S2 =
In the previous exercise there were two possible outcomes; reject the null hypothesis or fail to reject the null hypothesis. Explain in your own words what is meant by these outcomes.
We suspect that the average fasting blood sugar level of Mexican Americans is 108. A random sample of 225 clinic patients (all Mexican American) yields a mean blood sugar level of 119 (S2 = 100).
Again use the test in Exercise 9.9 to determine the power when the mean is 1.5 under the alternative hypothesis and the variance is again 5.
Use the test in Exercise 9.9 (i.e., critical values) to determine the power of the test when the mean is 1.0 under the alternative hypothesis, the variance is 5, and the sample size is 5.
Consider a sample of size 5 from a normal population with a variance of 5 and a mean of zero under the null hypothesis. Find the critical values for a 0.05 two-sided significance test of the mean
Suppose we would like to test the hypothesis that mean cholesterol levels of residents of Kalamazoo and Ann Arbor, Michigan, are the same. We know that both populations have the same variance. State
The Orange County Public Health Department was concerned that the mean daily fecal coliform level in a particular month at Huntington Beach, California, exceeded a safe level. Let us call this level
Using the data from Exercise 9.5, state the hypothesis set (null and alternative hypotheses) for testing whether the mean blood lead level of smelter workers exceeds that of clerical workers.
In the example cited in Exercise 9.3, the physician measures the blood lead levels of smelter workers in the same factory and finds their mean blood lead level to be 15.3. State the hypothesis set
Using the data from Exercise 9.3, state the hypothesis set (null and alternative hypotheses) for testing whether the population mean blood lead level exceeds 11.2. What is the name for this type of
In a factory where he conducted a research study, an occupational medicine physician found that the mean blood lead level of clerical workers was 11.2.State the null and alternative hypotheses for
Chapters 8 and 9 discussed methods for calculating confidence intervals and testing hypotheses, respectively. In what manner are parameter estimation and hypothesis testing similar to one another? In
The following terms were discussed in Chapter 9. Give definitions of them in your own words:a. Hypothesis testb. Null hypothesisc. Alternative hypothesisd. Type I errore. Type II errorf. p-value g.
In Exercise 8.18, how many individuals must you select to obtain the halfwidth of a 99% confidence interval no larger than 0.5 mmHg?
Change exercise 8.18 to assume there are 400 randomly selected individuals with a mean of 75 and standard deviation of 12. Construct a 99% confidence interval for the mean.
The mean diastolic blood pressure for 225 randomly selected individuals is 75 mmHg with a standard deviation of 12.0 mmHg. Construct a 95% confidence interval for the mean.
Repeat Exercise 8.16 for 99% confidence intervals.
The standard hemoglobin reading for normal males of adult age is 15 g/100 ml. The standard deviation is about 2.5 g/100 ml. For a group of 36 male construction workers, the sample mean was 16 g/100
The mean weight of 100 men in a particular heart study is 61 kg with a standard deviation of 7.9 kg. Construct a 95% confidence interval for the mean.
What would the number of experimental subjects have to be under the assumptions in Exercise 8.13 if you want to construct a 99% confidence interval with half-width no greater then 0.4? Under the same
Suppose you want to construct a 95% confidence interval for mean aggression scores as in Exercise 8.11, and you can assume that the standard deviation of the estimate is 5. How many experimental
Suppose the sample size in exercise 8.11 is 169 and the mean score is 55 with a standard deviation of 5. Construct a 99% confidence interval for the population mean.
In a sample of 125 experimental subjects, the mean score on a postexperimental measure of aggression was 55 with a standard deviation of 5. Construct a 95% confidence interval for the population mean.
Suppose that a sample of pulse rates gives a mean of 71.3, as in Exercise 8.9, with a standard deviation that can be assumed to be 9.4 (close to the estimate observed in exercise 8.9). How many
Suppose we randomly select 20 students enrolled in an introductory course in biostatistics and measure their resting heart rates. We obtain a mean of 66.9(S = 9.02). Calculate a 95% confidence
How can bootstrap confidence intervals be generated? Name the simplest form of a bootstrap confidence interval. Are bootstrap confidence intervals exact?
Explain the bootstrap principle. How can it be used to make statistical inferences?
Two situations affect the choice of a calculation of a confidence interval: (1)the population is known; (2) the population variance is unknown. How would you calculate a confidence interval given
State the advantages and disadvantages of using confidence intervals for statistical inference.
What are the desirable properties of a confidence interval? How do sample size and the level of confidence (e.g., 90%, 95%, 99%) affect the width of a confidence interval?
What are the advantages and disadvantages of using point estimates for statistical inference?
What are the desirable properties of an estimator of a population parameter?
In your own words define the following terms:a. Descriptive statisticsb. Inferential statisticsc. Point estimate of a population parameterd. Interval (confidence interval) estimate of a population
Assume that we have normally distributed data. From the standard normal table, find the probability area bounded by ±1 standard deviation units about a population mean and by ±1 standard errors
Based on a sample of six cases, the mean incubation period for a gastrointestinal disease is 26.0 days with a standard deviation of 2.83 days. The population standard deviation () is unknown, but
The following questions relate to comparisons between the standard normal distribution and the t distribution:a. What is the difference between the standard normal distribution (used to determine Z
Here are some questions about sampling distributions in comparison to the parent populations from which samples are selected:a. Describe the difference between the distribution of the observed sample
The following questions pertain to the central limit theorem:a. Describe the three main consequences of the central limit theorem for the relationship between a sampling distribution and a parent
Using the data from Exercise 7.8, for a sample of 25 female students, calculate the standard error of the mean, draw the sampling distribution about , and find:a. P(200 < X < 220)b. P(X < 196)c.
A health researcher collected blood samples from a population of female medical students. The following cholesterol measurements were obtained: = 211, = 44. If we select any student at random,
The average height of male physicians employed by a Veterans Affairs medical center is 180.18 cm with a standard deviation of 4.75 cm. Find the probability of obtaining a mean height of 184.93 cm or
Based on the findings obtained from Exercises 7.4 and 7.5, what general statement can be made regarding the effect of sample size on the probabilities for the sample means?
Repeat Exercise 7.4 with a sample size of 36.
The population mean () blood levels of lead of children who live in a city is 11.93 with a standard deviation of 3. For a sample size of 9, what is the probability that a mean blood level will be:a.
The average fasting cholesterol level of an entire community in Michigan is = 200 ( = 20). A sample (n = 25) is selected from this population. Based on the information provided, sketch the sampling
Calculate the standard error of the mean for the following sample sizes ( =100, = 10). Describe how the standard error of the mean changes as n increases.a. n = 4b. n = 9c. n = 16d. n = 25e. n = 36
Define in your own words the following terms:a. Central limit theoremb. Standard error of the meand. Student’s t statistic
It is suspected that a random variable has a normal distribution with a mean of 6 and a standard deviation of 0.5. After observing several hundred values, we find that the mean is approximately equal
The population of 25-year-old American women has a remaining life expectancy that is also normally distributed and differs from that of the males in Exercise 6.17 only in that the women’s average
Suppose that the population of 25-year-old American males has an average remaining life expectancy of 50 years with a standard deviation of 5 years and that life expectancy is normally distributed.a.
Assume the weights of women between 16 and 30 years of age are normally distributed with a mean of 120 pounds and a standard deviation of 18 pounds.If 100 women are selected at random from this
A community epidemiology study conducted fasting blood tests on a large community and obtained the following results for triglyceride levels (which were normally distributed): males— = 100, =
Repeat Exercise 6.12 again, but this time with a mean of 110 and a standard deviation of 15.
Repeat Exercise 6.12 but with a standard deviation of 9 instead of 12.
In a health examination survey of a prefecture in Japan, the population was found to have an average fasting blood glucose level of 99.0 with a standard deviation of 12. Determine the probability
The mean height of a population of girls aged 15 to 19 years in a northern province in Sweden was found to be 165 cm with a standard deviation of 15 cm. Assuming that the heights are normally
A first year medical school class (n = 200) took a first midterm examination in human physiology. The results were as follows (X = 65, S = 7). Explain how you would standardize any particular score
The inverse of Exercise 6.8 is to be able to find a Z score when you know a probability. Assuming a standard normal distribution, identify the Z score indicated by a # sign that is associated with
Another way to express probabilities associated with Z scores (assuming a standard normal distribution) is to use parentheses according to the format:P(Z > 0) = 0.5000, for the case when Z = 0.
The areas under a standard normal curve also may be considered to be probabilities.Find probabilities associated with the area:a. Above Z = 2.33b. Below Z = –2.58c. Above Z = 1.65 and below Z =
Determine the areas under the standard normal curve that fall between the following values of Z:a. 0 and 1.00b. 0 and 1.28c. 0 and –1.65d. 1.00 and 2.33e. –1.00 and –2.58
Referring to the properties shown in Table 6.3, find the standard normal score (Z score) associated with the following percentiles: (a) 5th, (b) 10th, (c)20th, (d) 25th, (e) 50th, (f) 75th, (g) 80th,
If you were a clinical laboratory technician in a hospital, how would you apply the principles of the standard normal distribution to define normal and abnormal blood test results (e.g., for
The following questions pertain to the standard normal distribution:a. How is the standard normal distribution defined?b. How does a standard normal distribution compare to a normal distribution?c.
The following questions pertain to some important facts to know about a normal distribution:a. What are three important properties of a normal distribution?b. What percentage of the values are:i.
Define the following terms in your own words:Continuous distribution Normal distribution Standard normal distribution Probability density function Standardization Standard score Z score Percentile
In the example in Section 5.9, consider the probability that three items have mismatched labels and one of these items is found.a. Calculate the probability that all three items would pass inspection
a. Define the probability density and cumulative probability function for an absolutely continuous random variable.b. Which of these functions is analogous to the probability mass function of a
Compute the mean and variance of the binomial distribution Bi(n, p). Find the arithmetic values for the special case in which both n = 10 and p = 1/2.
Under the conditions given for Exercise 5.18, calculate the probability that the child will have two dominant genes if:a. One of the parents is a carrier and the other parent has two dominant genesb.
Sickle cell anemia is a genetic disease that occurs only if a child inherits two recessive genes. Each child receives one gene from the father and one from the mother. A person can be characterized
For the binomial distribution, do the following:a. Give the conditions necessary for the binomial distribution to apply to a random variable.b. Give the general formula for the probability of r
Consider the following 2 × 2 table that shows incidence of myocardial infarction(denoted MI) for women who had used oral contraceptives and women who had never used oral contraceptives. The data in
Based on the following table of hemoglobin levels for miners, compute the probabilities described below. Assume that the proportion in each category for this set of 90 miners is the true proportion
Give a definition or description of the following:a. C(4, 2)b. P(5, 3)c. The addition rule for mutually exclusive eventsd. The multiplication rule for independent events
Provide definitions for each of these terms:a. Elementary eventsb. Mutually exclusive eventsc. Equally likely eventsd. Independent eventse. Random variable
In how many ways can four different colored marbles be arranged in a row?
Use Formula 5.8, combinations of r objects taken out of n, to determine the following combinations:a. C(7, 4)b. C(6, 4)c. C(6, 2)d. C(5, 2)e. What is the relationship between 5.11 (d) and 5.9 (e)?f.
Nine volunteers wish to participate in a clinical trial to test a new medication for depression. In how many ways can we select five of these individuals for assignment to the intervention trial?
Refer to Formula 5.7, permutations of r objects taken from n objects. Compute the following permutations:a. P(8, 3)b. P(7, 5)c. P(4, 2)d. P(6, 4)e. P(5, 2)
Repeat Exercise 5.4 but this time assume that the probability of having a male offspring is 0.514 and the probability of having a female offspring is 0.486. In this case, the elementary outcomes are
In an ablation procedure, the probability of acute success (determined at completion of the procedure) is 0.95 when an image mapping system is used.Without the image mapping system, the probably of
A pharmacist has filled a box with six different kinds of antibiotic capsules.There are a total of 300 capsules, which are distributed as follows: tetracycline(15), penicillin (30), minocycline (45),
What is the expected distribution—numbers and proportions—of each of the six faces (i.e., 1 through 6) of a die when it is rolled 1000 times?
A certain laboratory animal used in preclinical evaluations of experimental catheters gives birth to only one offspring at a time. The probability of giving birth to a male or a female offspring is
In the science exhibit of a museum of natural history, a coin-flipping machine tosses a silver dollar into the air and tallies the outcome on a counting device.What are all of the respective possible
In this exercise, we would like you to toss four coins at the same time into the air and record and observe the results obtained for various numbers of coin tosses. Count the frequencies of the
By using a computer algorithm, an investigator can assign members of twin pairs at random to an intervention condition in a clinical trial. Assume that each twin pair consists of dizygotic twins (one
Answer the following questions:a. Can a population have a zero variance?b. Can a population have a negative variance?c. Can a sample have a zero variance?d. Can a sample have a negative variance?
that it seems suspicious. Such extreme values are called outliers. Which estimate of location do you trust more when this observation is included, the mean or the median?
The eleventh observation of 931 is so different from all the others in Exercise
Which statistics varied the most from Exercise 4.19 to Exercise 4.20? Which statistics varied the least?

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