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biostatistics

Questions and Answers of Biostatistics

MCATs. Suppose that scores on the biological sciences section of the Medical College Admissions Test (MCAT) are Normally distributed with a mean of 9.2 and standard deviation of 2.2. Successful
BMI. Body mass index (BMI) is equal to “weight in kilograms”divided by “height in meters squared.” A study by the National Center for Health Statistics suggested that women between the ages
|Z| ≥ 2.56. What proportion of Standard Normal Z-values are greater than 2.56? What proportion are less than −2.56? What proportion are either below −2.56 or above 2.56?
College entrance exams. The SAT and ACT are standardized tests for college admission in the United States. Both tests include components that measure reading comprehension. Suppose that SAT critical
A six-foot seven-inch tall man. Have you ever wondered why a man who is 6′ 7″ tall (79″) seems so much taller than a man who is 5′ 10″(70″) even though he is only 13% taller in relative
Coliform levels (90th percentile). Exercise 7.14 addressed coliform levels in water samples from a particular site. The coliform levels were assumed to vary according to a Normal distribution with a
Gestation less than 32 weeks. Recall that uncomplicated human gestational length is approximately Normally distributed with μ = 39 weeks and σ = 2 weeks. What percentage of gestations are less than
Gestation (99th percentile). Recall that gestation in uncomplicated human pregnancies from conception to birth varies according to a Normal distribution (approximately so) with a mean of 39 weeks and
Z-percentiles. Find the following z-percentiles:(a) z0.10(b) z0.35(c) z0.74(d) z0.85(e) z0.999
Coliform levels. Water samples from a particular site demonstrate a mean coliform level of 10 organisms per liter with standard deviation 2. Values vary according to a Normal distribution. What
Alzheimer brains. The weight of brains from Alzheimer cadavers varies according to a Normal distribution with mean 1077 g and standard deviation 106 g.l The weight of an Alzheimer-free brain averages
Standard Normal proportions. Use Table B to find the proportion of a Standard Normal distribution that is:(a) below −1.42(b) above 1.42(c) below 1.25(d) between 1.42 and 1.25
z0.50= ? (Z table not required; use your knowledge of Standard Normal curves.)
In the notation zp, what does the subscript p represent?
Use the 68–95–99.7 rule to determine Pr(Z > −2). (Z table not required.)
Use the 68–95–99.7 rule to determine Pr(Z < −2). (Z table not required.)
Fill in these blanks: Z ~ N(____, ____)
Fill in the blank: The Standard Normal random variable is often referred to as a ____ variable. (Answer is a letter.)
What is the standard deviation of the Standard Normal distribution?
What is the mean of the Standard Normal distribution?
What does “X ~ N(μ, σ)” mean?
How many different Standard Normal distributions are there?
How many different Normal distributions are there?
Fill in the blank: The area under the curve to the left of a point on a Normal density corresponds to the _____________probability of that value.
Fill in the blank: The area under the curve between any two points on a Normal density curve corresponds to the _____________of values within that range.
What parameter controls the spread of the Normal curve?
What parameter controls the location of the Normal curve?
Normal pdfs have two parameters. Name them.
The total area under a Normal curve sums to exactly _____________.
Fill in the blanks: _____% of area under a Normal curve is within μ± σ, _____% is within μ ± 2σ, and ____% is within μ ± 3σ.
Fill in the blank: Normal curves have inflection points that are one _____________ above and below μ.
Fill in the blank: Normal distributions are centered on the value of _____________.
Death row inmate. An inmate on death row in the state of Illinois has a WAIS score of 51. What percentage of people have a score below this level?
Top 10 and 1% of the WAIS. How high must a WAIS score be to be in the top 10% of scores? How high must it be to rank in the top 1%?
Middle 50% of WAISs. Recall that the Wechsler Adult Intelligence Scale scores are calibrated to vary according to a Normal distribution with μ = 100 and σ = 15. What Wechsler scores cover the
64th percentile on a Normal z-curve. What is the 64th percentile on a Standard Normal distribution? What notation denotes this value?
45th percentile on a Standard Normal curve. What is the 45th percentile on a Standard Normal distribution? (Use Table B to look up z0.45.)
Heights of 20-year-olds. Heights of 20-year-old men vary approximately according to a Normal distribution with μ = 176.9 cm and σ = 7.1 cm.(a) What percentage of U.S. men are at least 6 feet tall?
Heights of 10-year-old boys. We’ve established that heights of 10-year-old boys vary according to a Normal distribution with μ =138 cm and σ = 7 cm.(a) What proportion of this population is less
Visualizing the distribution of gestational length. The gestation length illustrative example presented earlier in this chapter established that uncomplicated pregnancies vary according to a Normal
Height of 10-year-olds. This exercise continues the work we began in the prior exercise. What range of values will capture the middle 95% of heights? How tall are the tallest 2.5%?
Heights of 10-year-olds. Heights of 10-year-old male children follow a Normal distribution with μ =138 centimeters and σ = 7 centimeters.j Create a sketch of a Normal curve depicting this
Random 7s. The digits (0 through 9) in Appendix Table A occur randomly throughout the table. Thus, a value of 7 has a 0.1 chance of occurring in any single slot anywhere in the table.(a) Each line in
Human papillomavirus. In a particular population, 20% of the individuals are human papillomavirus carriers. Select four individuals at random from this population.(a) Build the pmf for the number of
False positives. A rapid screening test for HIV has a false positive rate of 0.5%. This means that the probability of a false positive test is 0.005. If the test is used in 500 HIV-free individuals,
Decayed teeth. A child has 20 deciduous teeth. Two of her teeth are decayed. Given that this is all that you currently know about the child’s dentition, how many different possible combinations of
Electromagnetic fields. Twenty-five percent of the children in a community are exposed to high levels of electromagnetic field(EMF) radiation. You select at random a control series of 20 children
Linda’s omelets. Linda hears a story on National Public Radio stating that one in six eggs in the United States are contaminated with Salmonella. If Salmonella contamination occurs independently
Herpes simplex-2. Suppose 7.5% of a population is infected with Herpes simplex-2 virus (HSV2). You select seven individuals at random from the population. What is the probability of finding at least
Prevalence 10%. The prevalence of a condition in a population is 10%. You take a simple random sample of 15 people from this population. Let X represent the number of individuals in the sample with
Smoking on campus. Suppose 20% of the students on campus smoke. You select two students at random. In what percentage of samples will both students be smokers?
Prevalence 76.8%. The prevalence of a trait is 76.8%.(a) In a simple random sample of n = 5, how many individuals are expected to exhibit this characteristic?(b) How many would you expect to see with
Fill in the blank: The expected number of successes μ for a binomial random variable X ~ (n, p) is equal to n × ____.
What symbol is used to represent the variance of a binomial distribution?
What symbol is used to represent the mean (expected value) of a binomial distribution?
Fill in the blank: Pr(X ≤ x) represents the _____________ probability of x.
What does q represent in the context of binomial distributions?
Determine the value of 7!/6! without using a calculator.
By definition, 0! = ____
How do you read the statement “X ~ b(n, p)”?
How do you read the statement “Pr(X = x)”?
What does x represent in the statement Pr(X = x)?
What does X represent in the statement Pr(X = x)?
What does “4C2= 6” mean in plain language?
What does the symbol p represent in the statement X ~ b(n, p)?
What does the symbol n represent in the statement X ~ b(n, p)?
What does the symbol ~ represent in the statement X ~ b(n, p)?
What does the symbol X represent in the statement X ~ b(n, p)?
Binomial distributions have two parameters. Name them.
Telephone survey. Exercise 6.5 introduced a random digit dialing machine with p = 0.15 for each call attempt.(a) What is the expected value and variance for the number of contacts in eight
Tay-Sachs. Exercises 6.1 and 6.3 considered the random number of Tay-Sachs cases in three pregnancies from a carrier couple (X ~ b(3, 0.25)). What is the expected value and variance of this random
Telephone survey, two or fewer. In the telephone survey technique introduced in Exercise 6.5, what is the probability of two or fewer successful calls in eight attempts?
Telephone survey. A telephone survey uses a random digit dialing machine to call subjects. The random digit dialing machine is expected to reach a live person 15% of the time. In eight attempts, what
Tay-Sachs couples. Approximately 1 in 28 people of Ashkenazi Jewish descent are Tay-Sachs carriers. In randomly sampling one man and one woman from this population, what is the probability neither is
Tay-Sachs inheritance. Exercise 6.1 introduced facts about TaySachs inheritance. If both parents are carriers, there is a one in four chance the offspring inherits both alleles necessary for
Breast cancer. Say the lifetime probability of developing female breast cancer in a population is 1 in 10. Let X represent the number of women among 5102 women, selected randomly from this
Tay-Sachs. Tay-Sachs is a metabolic disorder that is inherited as an autosomal recessive trait. Both recessive alleles are necessary for expression of the disease. Therefore, when each parent is a
16. Goodyer and Altham (A-26) compared the number of lifetime exit events occurring over the lives of children between the ages of 7 and 16 years who recently experienced new onset episodes of
15. Sinton et al. (A-25) reported the following data regarding the incidence of antisperm antibodies in female infertility patients and their husbands.Antibody Status of Husband Antibody Status of
14. Explain how researchers interpret the following measures:a. Relative riskb. Odds ratioc. Mantel—Haenszel common odds ratio
13. Under what conditions is the Mantel—Haenszel test appropriate?
12. Define the following:a. Observational studyf. Relative riskb. Risk factor g. Oddsc. Outcome h. Odds ratiod. Retrospective study i. Confounding variablee. Prospective study
11. When do researchers use the Fisher exact test rather than the chi-square test?
10. Explain the rationale behind the method of computing the expected frequencies in a test of homogeneity.
9. Explain the difference between a test of independence and a test of homogeneity.
8. Explain the rationale behind the method of computing the expected frequencies in a test of independence.
7. How are the degrees of freedom computed when an X2 value is computed from a contingency table?
6. What is a contingency table?
5. How does one adjust for small expected frequencies?
4. State Cochran's rule for small expected frequencies in goodness-of-fit tests.
3. Explain how the degrees of freedom are computed for the chi-square goodness-of-fit tests.
2. What are the mean and variance of the chi-square distribution?
1. Explain how the chi-square distribution may be derived.
13. Find a published article in the health sciences field in which each of the following techniques is employed:a. Dummy variable codingb. Stepwise regressionc. Logistic regression
12. Give an example in your field in which logistic regression analysis would be appropriate when the independent variable is continuous.
11. Give an example in your field in which logistic regression analysis would be appropriate when the independent variable is dichotomous.
10. What is an odds ratio?
9. Define the word odds.
8. Write out and explain the components of the logistic regression model.
7. When is logistic regression used?

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