Richard J. Rossi - Applied Biostatistics for the Health Sciences

17 2.17Is themean sensitive to the extreme values in the population?median sensitive to the extreme values in the population?

18 2.18Suppose the population of 250 doctors at a public hospital has been classified according to the variables Age and Gender and is summarized in the table below.25–4041–5556–70Male546642Female244123Determine the percentage of doctors at this hospital that are female.Determine the percentage of doctors at this hospital that are aged 56 or older.Determine the percentage of doctors at this hospital that are female and aged 41 or older.Determine the percentages of doctors at this hospital in each age group.Determine the age group that the median age falls in.

19 2.19Describe how the geometric mean (GM) is computed and why it might be used in place of the arithmetic mean.

20 2.20 What are three parameters that measure thetypical values in a population.the spread of a population.

21 2.21Which of the parametersmeasuring the typical value in a population are not sensitive to the extreme values in a population?measuring the spread of a population are not sensitive to the extreme values in a population?

22 2.22 According to the article “Mean body weight, height, waist circumference, and body mass index among adults: United States, 1999 – 2000 through 2015 – 2016” published in National Health Statistics Report (Fryar, 2018), the estimated mean weight of an adult male in the United States in 2015 – 2016 was 197.8. Suppose the distribution of weights of adult males is a mound shaped distribution with mean µ = 200 and standard deviation σ = 25. Determinethe weight range that approximately 95% of the adult males in the United States in 2015 – 2016 fall in.the coefficient of variation for the weights of adult males in the United States in 2015 – 2016.

23 2.23For a mound-shaped distribution what is the approximate percentage of the population fallingbetween the values μ−2σ and μ+2σ.above the value μ+3σ.below the value μ−σ.

24 2.24Which parameter measures the relative spread in a population? How is this parameter computed?

25 2.25 What does it mean whenthe median is much larger than the mean?there is a large distance between the 25th and 75th percentiles?there is a large distance between the 75th and 99th percentiles?

26 2.26In the article “Mean body weight, height, waist circumference, and body mass index among adults: United States, 1999 – 2000 through 2015 – 2016” published in National Health Statistics Report (Fryar, 2018), the statistics in Table 2.15 were reported for adult females in the United States for 2015 – 2016. Use the information in Table 2.15 to answer the following questions. Table 2.15 The Approximate Means and Standard Deviations for the Variables Weight, Height, and Body Mass Index for Adult Females in the U.S. for 2015 – 2016 for Exercise 2.27VariableMeanStandard DeviationWeight169.8 lbs20 lbsHeight63.6 inches3 inchesBMI29.64Compute the coefficient of variation for the variable weight.Compute the coefficient of variation for the variable height.Compute the coefficient of variation for the variable BMI.

27 2.27What does it mean when the value of the correlation coefficient for two quantitative variables isρ=−1.ρ = 0.ρ = 1.

28 2.28 What does the correlation coefficient measure?

29 2.29What are the units of the correlation coefficient?

30 2.30What does it mean when two events are said to beindependent events?dependent events?

31 2.31Under what conditions is the probability of the event “A or B” equal to the sum of their respective probabilities?

32 2.32Under what conditions is the probability of the event “A and B” equal to the product of their respective probabilities?

33 2.33Suppose that P(A)=0.54,P(B)=0.48, and P(A and B)=0.33. Determinethe probability that the event A does not occur.the probability that the event A or B occurs.the probability that neither event A nor event B occurs.the conditional probability that event A occurs given that the event B will occur.the conditional probability that event B occurs given that the event A will occur.whether or not the events A and B are independent events.

34 2.34Suppose that P(A)=0.60,P(B)=0.25, and the events A and B are disjoint events. Determinethe probability that event A does not occur.the probability that event A or B occurs.the probability that neither event A nor event B occurs.the conditional probability that event A occurs given that the event B will occur.whether or not the events A and B are independent events.

35 2.35Suppose that P(A)=0.6,P(B)=0.8 and A and B are independent events. Determinethe probability that the event B does not occur.the probability that the event A and B occurs.the probability that the event A or B occurs.the conditional probability that the event A occurs given the event B will occur.the conditional probability that the event B occurs given the event A will occur.

36 2.36Of the people who have had a heart attack, suppose that 80% change their diet, 42% get more exercise, and 36% change their diet and get more exercise. Determine the probability that a randomly selected individual who has had a heart attackdoes not get more exercise.changes their diet or gets more exercise.gets more exercise given they change their diet.

37 2.37In the article “Prevalence and predictability of low-yield inpatient laboratory diagnostic tests” published in JAMA Network Open (Xu, 2019), the authors reported the prevalence, sensitivity, and specificity for diagnosing normal troponin I levels; troponin I is a marker for acute myocardial infarction. The authors reported a prevalence of 0.33, a sensitivity of 0.88, and a specificity of 0.79 for the lab test for troponin I levels. Determine thepositive predictive value (PPV) for this test.negative predictive value (NPV) for this test.

38 2.38According to the Medscape Today article “Standard care for pap screening” (Lie, 2003), the sensitivity and specificity of the pap smear test are at least 0.29 and 0.97, respectively. If the prevalence of cervical cancer is 0.01, determinethe probability that a woman has a positive test result.the positive predictive value of the pap smear diagnostic test.the negative predictive value of the pap smear diagnostic test.

39 2.39In the article “Diagnostic testing for Lyme disease: beware of false positives” published in BC Medical Journal (Kling, 2015), the authors reported the sensitivity and specificity for two diagnostic tests, a two-step diagnostic test and a standard laboratory test, shown in Table 2.16. Assuming the prevalence of Lyme disease is 0.01, determine Table 2.16 The Sensitivity and Specificity for Two Tests for Diagnosing Lyme Disease in Exercise 2.40TestSensitivitySpecificityTwo-step0.870.99Lab Test0.700.73the positive predictive value of the two-step diagnostic test.the negative predictive value of the two-step diagnostic test.the positive predictive value of the laboratory diagnostic test.the negative predictive value of the laboratory diagnostic test.

40 2.40According to the American Red Cross, the percentage of people in the United States having blood type O is 38%. If four people from the United States are selected at random and independently, determine the probability thatnone have blood type O.all four have blood type O.at least one has blood type O.

41 2.41The autosomal recessive genetic disorder sickle cell anemia is caused by a defect in the hemoglobin beta (HBB) gene. Two defective genes, denoted by SS, are needed for sickle cell anemia to occur in an individual. If each parent carries one sickle HBB gene (S) and one normal HBB gene (A), and a child receives exactly one gene independently from each parent, determinethe probability that a child will have sickle cell anemia.the probability that a child will not have sickle cell anemia.the probability that a child will not have any sickle HBB genes.