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biostatistics

Questions and Answers of Biostatistics

For each of the following sampling situations indicate whether the sampling distribution of the sample proportion can be approximated by a normal distribution and explain why or why not. (a) p = .50,
For each of the following populations of measurements, state whether the sampling distribution of the sample mean is normally distributed, approximately normally distributed, or not approximately
Refer to Exercise 25. What is the probability that a single simple random sample of size 35 drawn from this population will yield a mean between 22 and 29?
Refer to Exercise 25. What will be the mean and variance of the sampling distribution?
In a population of subjects who died from lung cancer following exposure to asbestos, it was found that the mean number of years elapsing between exposure and death was 25. The standard deviation was
Refer to Exercise 22. What is the probability that a single simple random sample of size 110 drawn from this population will yield a sample proportion smaller than .50?
Refer to Exercise 22. Compute the mean and variance of the sampling distribution.
It is estimated by the 1999–2000 NHANES (A-7) that among adults 18 years old or older 53 percent have never smoked. Assume the proportion of U.S. adults who have never smoked to be .53.Consider the
How many simple random samples (without replacement) of size 5 can be selected from a population of size 10?
Use the information in Review Exercises 18 and 19 to find the probability that the difference in the cancer percentages between men and women will be less than 5 percent when 220 women and 250 men
Refer to Review Exercise 17. The cancer rate for men ages 65 and older is 23 percent. Use this estimate as the percentage of all men ages 65 and older who have been told by a health care provider
Refer to Review Exercise 17. The reported cancer rate for women subjects ages 65 and older is 17 percent. Using this estimate as the true percentage of all females ages 65 and over who have been told
The results of the 1999 National Health Interview Survey released in 2003 (A-7) showed that among U.S. adults ages 60 and older, 19 percent had been told by a doctor or other health care provider
Using the information in Review Exercises 14 and 15, and assuming independent random samples of size 100 and 120 for women and men, respectively, find the probability that the difference in sample
Refer to Review Exercise 14. The mean iron level for men between the ages of 20 and 39 years is 17.9 mg with an estimated standard deviation of 10.9 mg. Using 17.9 and 10.9 as population parameters,
In the results published by Wright et al. (A-2) based on data from the 1999–2000 NHANES study referred to in Exercises 5.4.1 and 5.4.2, investigators reported on their examination of iron levels.
Using the information in Review Exercises 11 and 12, find the probability that the difference in mean BMI for 45 women and 50 men selected independently and at random from the respective populations
In the study cited in Review Exercise 11, the researchers reported the mean BMI for men ages 60 and older with normal skeletal muscle index to be 24.7 with a standard deviation of 3.3.Using these
Janssen et al. (A-10) studied Americans ages 60 and over. They estimated the mean body mass index of women over age 60 with normal skeletal muscle to be 23.1 with a standard deviation of 3.7. Using
Suppose it is known that the response time of healthy subjects to a particular stimulus is a normally distributed random variable with a mean of 15 seconds and a variance of 16. What is the
Explain the procedure you would follow in constructing the sampling distribution of the difference between sample proportions based on large samples from finite populations.
Describe the sampling distribution of the difference between two sample means when large samples are drawn.
Describe the sampling distribution of the sample proportion when large samples are drawn.
Describe the sampling distribution of the difference between two sample means.
How does the sampling distribution of the sample mean, when sampling is without replacement, differ from the sampling distribution obtained when sampling is with replacement?
Explain the central limit theorem.
Describe the sampling distribution of the sample mean when sampling is with replacement from a normally distributed population.
Explain how a sampling distribution may be constructed from a finite population.
What is a sampling distribution?
Explain why each of the following distributions is or is not a probability distribution: (a) (b) x P(X = x) x P(X = x) 01234 0.15 0 0.15 0.25 1 0.20 0.10 2 0.30 0.25 3 0.10 0.30 (c) = 0 P(X = x) 0.15
Explain why each of the following measurements is or is not the result of a Bernoulli trial:(a) The number of surgical procedures performed in a hospital in a week(b) A hospital patient’s
Explain why each of the following measurements is or is not the result of a Bernoulli trial:(a) The gender of a newborn child(b) The classification of a hospital patient’s condition as stable,
Given the normally distributed random variable X with m = 30 P1X … 502 = .9772, s.
Given the normally distributed random variable X with m = 25 P1X … 102 = .0778, s.
Given the normally distributed random variable X with s = 5 P1X Ú 252 = .0526, m.
Given the normally distributed random variable X with s = 15 P1X … 502 = .9904, m.
Given the normally distributed random variable X with s = 10 P1X … 402 = .0080, m.
Given the normally distributed random variable X with mean 100 and standard deviation 15, find the numerical value of k such that: (a) P(X k) = .0094 (b) P(X k) = .1093 (c) P(100 X k) = .4778 (d)
Given the normally distributed random variable X, find the numerical value of k such tha P1m - ks … X … m + ks2 = .754.
Suppose a variable X is normally distributed with a standard deviation of 10. Given that .0985 of the values of X are greater than 70, what is the mean value of X?
Given a binomial variable with a mean of 20 and a variance of 16, find n and p.
Scores made on a certain aptitude test by nursing students are approximately normally distributed with a mean of 500 and a variance of 10,000.(a) What proportion of those taking the test score below
A nurse supervisor has found that staff nurses, on the average, complete a certain task in 10 minutes.If the times required to complete the task are approximately normally distributed with a standard
The IQs of individuals admitted to a state school for the mentally retarded are approximately normally distributed with a mean of 60 and a standard deviation of 10.(a) Find the proportion of
In a study of the relationship between measles vaccination and Guillain-Barré syndrome (GBS), Silveira et al. (A-16) used a Poisson model in the examination of the occurrence of GBS during latent
A Harris Interactive poll conducted in Fall, 2002 (A-15) via a national telephone survey of adults asked, “Do you think adults should be allowed to legally use marijuana for medical purposes if
On the average, two students per hour report for treatment to the first-aid room of a large elementary school.(a) What is the probability that during a given hour three students come to the first-aid
In a study by Thomas et al. (A-14) the Poisson distribution was used to model the number of patients per month referred to an oncologist. The researchers use a rate of 15.8 patients per month that
In a poll conducted by the Pew Research Center in 2003 (A-13), a national sample of adults answered the following question, “All in all, do you strongly favor, favor, oppose, or strongly oppose . .
Kanjanarat et al. (A-12) estimate the rate of preventable adverse drug events (ADEs) in hospitals to be 35.2 percent. Preventable ADEs typically result from inappropriate care or medication errors,
Using the data of your answer to Question 13, demonstrate the use of the standard normal distribution in answering probability questions related to the variable selected.
Give an example of a random variable that you think is, at least approximately, normally distributed.
Describe the standard normal distribution and tell how it is used in statistics.
Describe the normal distribution.
Give an example of a random variable that you think is distributed according to the Poisson law.
Describe the Poisson distribution.
Give an example of a random variable that you think follows a binomial distribution.
Describe the binomial distribution.
What is a cumulative probability distribution?
Define the probability distribution of a continuous random variable.
Define the probability distribution of a discrete random variable.
What is a continuous random variable? Give three examples of interest to the health professional.
What is a discrete random variable? Give three examples that are of interest to the health professional.
Create a table that cross-tabulates the counts of each mother’s marital status (MARITAL) and whether she had a low birth weight baby (LOW).(a) Find the probability a mother selected at random in
Create a table that cross-tabulates the counts of mothers in the classifications of whether the baby was premature or not (PREMIE) and whether the mother admitted to smoking during pregnancy(SMOKE)
The sensitivity of a screening test is .95, and its specificity is .85. The rate of the disease for which the test is used is .002. What is the predictive value positive of the test?
Verma et al. (A-14) examined the use of heparin-PF4 ELISA screening for heparin-induced thrombocytopenia(HIT) in critically ill patients. Using C-serotonin release assay (SRA) as the way of
Rothenberg et al. (A-13) investigated the effectiveness of using the Hologic Sahara Sonometer, a portable device that measures bone mineral density (BMD) in the ankle, in predicting a fracture.They
Refer to Exercise 18. State in words the meaning of the following events: (a) A (b) B (c) C
Refer to Exercise 18. State in words the meaning of the following events: (a) AUB (b) A B (c) ANC (d) AUC
For a certain population we define the following events with respect to plasma lipoprotein levels (mgdl): A = (10–15); B = 1Ú302; C = 1…202. Are the events A and B mutually exclusive? A and C?
Refer to Exercise 14. Comment on the event G = 1A ¨ B2.
Refer to Exercise 14. State in words the event F = 1B ´ C2.
Refer to Exercise 14. State in words the event E = 1A ´ B2.
For a certain population we define the following events for mother’s age at time of giving birth:A under 20 years; B 20–24 years; C 25–29 years; D 30–44 years. Are the events A, B, C, and D
The probability that a person selected at random from a population will exhibit the classic symptom of a certain disease is .2, and the probability that a person selected at random has the disease is
In a certain population of women 4 percent have had breast cancer, 20 percent are smokers, and 3 percent are smokers and have had breast cancer. A woman is selected at random from the population.What
Suppose that 3 percent of the people in a population of adults have attempted suicide. It is also known that 20 percent of the population are living below the poverty level. If these two events are
For a variety of reasons, self-reported disease outcomes are frequently used without verification in epidemiologic research. In a study by Parikh-Patel et al. (A-12), researchers looked at the
If the probability that a public health nurse will find a client at home is .7, what is the probability(assuming independence) that on two home visits made in a day both clients will be home?
Pillmann et al. (A-11) studied patients with acute brief episodes of psychoses. The researchers classified subjects into four personality types: obsessoid, asthenic/low self-confident, asthenic/high
Swor et al. (A-10) looked at the effectiveness of cardiopulmonary resuscitation (CPR) training in people over 55 years old. They compared the skill retention rates of subjects in this age group who
Coughlin et al. (A-9) examined the breast and cervical screening practices of Hispanic and non-Hispanic women in counties that approximate the U.S. southern border region. The study used data from
Name and explain the three properties of probability.
Define the following:(a) Probability (b) Objective probability(c) Subjective probability (d) Classical probability(e) The relative frequency concept of probability (f) Mutually exclusive events(g)
Calculate the skewness and kurtosis of the data set. What do they indicate?
Construct side-by-side box-and-whisker plots for the variable of MAGE for women who are and are not married. Do you see a difference in ages in the two groups? Which group has more variability?Are
Construct side-by-side box-and-whisker plots for the variable of TOUNCES for women who admitted to smoking and women who did not admit to smoking. Do you see a difference in birth weight in the two
Construct box-and-whisker plots for all four variables.
Do the histograms for TOUNCES and TGRAMS look strikingly similar? Why?
For each, construct a histogram and comment on the shape of the distribution.
Calculate the mean, median, standard deviation, IQR, and range.
Thilothammal et al. (A-19) designed a study to determine the efficacy of BCG (bacillus Calmette-Guérin) vaccine in preventing tuberculous meningitis. Among the data collected on each subject was a
Refer to Exercise 2.3.12. Compute the mean, median, variance, standard deviation, first quartile, third quartile, and interquartile range. Construct a boxplot of the data. Are the mode, median, and
Refer to Exercise 2.3.11. Compute the mean, median, variance, standard deviation, first quartile, third quartile, and interquartile range. Construct a boxplot of the data. Are the mode, median, and
Indicate for the following variables which you think would be a better measure of central tendency, the mean, the median, or mode, and justify your choice:(a) Annual incomes of licensed practical
Give a health sciences–related example of a population of measurements for which the median would be a better measure of central tendency than the mean.
Give a health sciences–related example of a population of measurements for which the mean would be a better measure of central tendency than the median.
On a statistics test students were asked to construct a frequency distribution of the blood creatine levels (units/liter) for a sample of 300 healthy subjects. The mean was 95, and the standard
Consider the following possible class intervals for use in constructing a frequency distribution of serum cholesterol levels of subjects who participated in a mass screening:Which set of class

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