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biostatistics

Questions and Answers of Biostatistics

Given a normally distributed population with a mean of 100 and a standard deviation of 20, find the following probabilities based on a sample of size 16:(a) Pð Þ x 100 (b) Pð Þ x 110(c) Pð
In the study cited in Exercise 5.3.4, researchers found the mean sodium intake in men and women 60 years or older to be 2940 mg with a standard deviation of 1476 mg. Use these values for the mean and
Wright et al. [A-2] used the 1999–2000 National Health and Nutrition Examination Survey(NHANES) to estimate dietary intake of 10 key nutrients. One of those nutrients was calcium(mg). They found in
If the uric acid values in normal adult males are approximately normally distributed with a mean and standard deviation of 5.7 and 1 mg percent, respectively, find the probability that a sample of
The study cited in Exercise 5.3.1 reported an estimated mean serum cholesterol level of 183 for women aged 20–29 years. The estimated standard deviation was approximately 37.Use these estimates as
The National Health and Nutrition Examination Survey of 1988–1994 (NHANES III, A-1) estimated the mean serum cholesterol level for U.S. females aged 20–74 years to be 204 mg/dl. The estimate of
understand the basic concepts of sampling with replacement and without replacement.
understand the central limit theorem and when to apply it.
understand how to use a sampling distribution to calculate basic probabilities.
be able to construct a sampling distribution of a statistic.
Explain why each of the following distributions is or is not a probability distribution:(a)x P Xð Þ ¼ x 0 0.15 1 0.25 2 0.10 3 0.25 4 0.30(b)x P Xð Þ ¼ x 0 0.15 1 0.20 2 0.30 3 0.10(c) x P Xð
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 ¼ 30 and P Xð Þ¼ 50 :9772, find s.
Given the normally distributed random variable X with m ¼ 25 and P Xð Þ¼ 10 :0778, find s.
Given the normally distributed random variable X with s ¼ 5 and P Xð Þ¼ 25 :0526, find m.
Given the normally distributed random variable X with s ¼ 15 and P Xð Þ¼ 50 :9904, find m.
Given the normally distributed random variable X with s ¼ 10 and P Xð Þ¼ 40 :0080, find 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 Xð Þ¼ k :0094(b) P Xð Þ¼ k :1093(c) Pð Þ 100 X k ¼
Given the normally distributed random variable X, find the numerical value of k such that Pð Þ m ks X m þ ks ¼ :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-Barre 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.
The weights of a certain population of young adult females are approximately normally distributed with a mean of 132 pounds and a standard deviation of 15.Find the probability that a subject selected
Given a normally distributed population with a mean of 75 and a variance of 625, find:(a) Pð Þ 50 x 100 (b) P xð Þ > 90(c) P xð Þ < 60 (d) P xð Þ 85(e) Pð Þ 30 x 110
If the total cholesterol values for a certain population are approximately normally distributed with a mean of 200 mg=100 ml and a standard deviation of 20 mg=100 ml, find the probability that an
Suppose the average length of stay in a chronic disease hospital of a certain type of patient is 60 days with a standard deviation of 15.Ifit is reasonable to assume an approximately normal
One of the variables collected in the North Carolina Birth Registry data (A-3) is pounds gained during pregnancy. According to data from the entire registry for 2001, the number of pounds gained
In the study of fingerprints, an important quantitative characteristic is the total ridge count for the 10 fingers of an individual. Suppose that the total ridge counts of individuals in a certain
For another subject (a 29-year-old male) in the study by Diskin et al. (A-11), acetone levels were normally distributed with a mean of 870 and a standard deviation of 211 ppb. Find the probability
In a certain population an average of 13 new cases of esophageal cancer are diagnosed each year. If the annual incidence of esophageal cancer follows a Poisson distribution, find the probability that
In a study of the effectiveness of an insecticide against a certain insect, a large area of land was sprayed. Later the area was examined for live insects by randomly selecting squares and counting
If the mean number of serious accidents per year in a large factory (where the number of employees remains constant) is five, find the probability that in the current year there will be:(a) Exactly
Tubert-Bitter et al. (A-9) found that the number of serious gastrointestinal reactions reported to the British Committee on Safety of Medicine was 538 for 9,160,000 prescriptions of the
Singh et al. (A-8) looked at the occurrence of retinal capillary hemangioma (RCH) in patients with von Hippel–Lindau (VHL) disease. RCH is a benign vascular tumor of the retina. Using a
Given the binomial parameters p ¼ :8 and n ¼ 3, show by means of the binomial expansion given in Table 4.3.1 that Pf xð Þ ¼ 1.
In a survey of nursing students pursuing a master’s degree, 75 percent stated that they expect to be promoted to a higher position within one month after receiving the degree. If this percentage
Coughlin et al. (A-6) estimated the percentage of women living in border counties along the southern United States with Mexico (designated counties in California, Arizona, New Mexico, and Texas) who
Suppose we were to take a simple random sample of 25 adults today and find that two have been tested for HIVat some point in their life. Would these results be surprising? Why or why not?
Refer to Exercise
Find the mean and variance of the number of people tested for HIV in samples of size 15.
Refer to Exercise
The same survey database cited in exercise 4.3.1(A-5) shows that 32 percent of U.S. adults indicated that they have been tested for HIVat some point in their life. Consider a simple random sample of
Suppose we select a simple random sample of five adults. Use Equation 4.3.2 to find the probability that, in the sample, the number of people who have been told that they have hypertension will
Refer to Exercise
How many adults who have been told that they have hypertension would you expect to find in a sample of 20?
Refer to Exercise
Based on data collected by the National Center for Health Statistics and made available to the public in the Sample Adult database (A-5), an estimate of the percentage of adults who have at some
Find the mean, variance, and standard deviation of this frequency distribution.
Refer to Exercise
Refer to Exercise 4.2.1.(a) What is probability that an individual selected at random used five addictive substances?(b) What is the probability that an individual selected at random used fewer than
summarizes the frequency distribution for this random variable.(a) Construct a table of the relative frequency and the cumulative frequency for this discrete distribution.(b) Construct a graph of the
In a study by Cross et al. (A-2), patients who were involved in problem gambling treatment were asked about co-occurring drug and alcohol addictions. Let the discrete random variable X represent the
be able to explain the similarities and differences between distributions of the discrete type and the continuous type and when the use of each is appropriate.
understand selected continuous distributions and how to use them to calculate probabilities in real-world problems.
understand selected discrete distributions and how to use them to calculate probabilities in real-world problems.
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?Exercises for Use
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) A [ B (b) A \ B (c) A \ C (d) A [ C
For a certain population we define the following events with respect to plasma lipoprotein levels(mg=dl): A ¼ (10–15); B ¼ ð 30Þ; C ¼ ð 20Þ. Are the events A and B mutually exclusive? A and
Refer to Exercise 14.Comment on the event G ¼ ðA \ BÞ.
Refer to Exercise 14.State in words the event F ¼ ðB [ CÞ.
Refer to Exercise 14.State in words the event E ¼ ðA [ BÞ.
For a certain population we define the following events for mother’s age at time of giving birth: A ¼under 20 years; B ¼ 20–24 years; C ¼ 25–29 years; D ¼ 30–44 years. Are the events A,
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
In a certain population the probability that a randomly selected subject will have been exposed to a certain allergen and experience a reaction to the allergen is .60. The probability is .8 that a
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?
The following table shows 1000 nursing school applicants classified according to scores made on a college entrance examination and the quality of the high school from which they graduated, as rated
A certain county health department has received 25 applications for an opening that exists for a public health nurse. Of these applicants 10 are over 30 and 15 are under 30.Seventeen hold
Pillman et al. (A-11) studied patients with acute brief episodes of psychoses. The researchers classified subjects into four personality types: obsessiod, 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 nonHispanic women in counties that approximate the U.S. southern border region. The study used data from the
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)

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