PubHlth Introductory Biostatistics Practice Test I (Without Unit 3 Questions)

Transcription

1 1 PubHlth Introductory Biostatistics Practice Test I (Without Unit 3 Questions) 1. (10 points) In the Honolulu Heart Study, Systolic Blood Pressure was tabulated for 100 Subjects including 37 Smokers and 63 Non-smokers, with the results given in the first table below. A stem and leaf plot of the 63 nonsmokers systolic blood pressure is given in the second table below. Table. Comparison of Systolic Blood Pressure Between Smokers and Nonsmokers from a Subset of 100 Subjects Relative Frequency (%) Cumulative Relative Frequency (%) Class Interval Nonsmokers Smokers Nonsmokers Smokers Table. Stem and Leaf Display of Systolic Blood Pressures of 63 Nonsmokers from the Honolulu Heart Study Stem

2 2 a. (2 points). What is the scale of measurement for systolic blood pressure? b. (2 points) Construct a figure that displays simultaneously the cumulative relative frequency distribution for nonsmokers and smokers. c. (2 points) Using your answer to part b, estimate the interquartile range for nonsmokers. d. (2 points) Using Table 2, what is the median systolic blood pressure among non-smokers? e. (2 points) Construct a box plot for systolic blood pressure among non-smokers.

3 3 2. (10 points) omitted as this was a Topic 3 question. 3. (10 points) omitted as this was a Topic 3 question. 4. (10 points) a. (2 points) As you probably already know, there are four human blood types, corresponding to the four mutually exclusive genetic phenotypes: O, A, B, and AB. Suppose 5400 individuals are examined and the frequency of each blood type is as shown in the table below. What is the relative frequency of each blood type? Blood Type Frequency O 2672 A 2041 B 486 AB 201 b. (2 points) Next assume that each of the 5400 individuals in part a has the same chance of being encountered. Estimate the probability of encountering a person with type A or type AB blood. c. (2 points) Consider a cross-tabulation of peas and their flower coloring akin to Mendel s famous hybridization experiments. Color of Flower Color of Pod Purple White Green 5 3 Yellow 4 2 If two of the peas are selected without replacement, what is the probability that the first is a green pod and the second is a yellow pod? d. (4 points) In a technique called acceptance sampling, a sample of items is randomly selected without replacement from a batch and tested. If at least one item in the sample fails, then the entire batch is rejected. Suppose a manufacturing company has manufactured a batch of 2500 aspirin tablets and 2% are defective. If 4 tablets are selected and tested, what is the probability that the entire batch will be rejected?

4 4 5. (10 points) A sample of data is summarized and has mean = 45, median = 21, sample standard deviation = 15, sample variance = 225, and interquartile range = 32 a. (5 points) If a constant c=10 is added to each value in the sample, what are the values of New mean = New median = New standard deviation = New sample variance = New interquartile range = b. (5 points) If a constant c=2 is multiplied to each value in the sample, what are the values of New mean = New median = New standard deviation = New sample variance = New interquartile range =

5 5 6. (10 points) A class of 43 students was given a test with 10 questions. The table below is a summary of the test scores; 2 students got all 10 questions correct, 8 students got 9 questions correct, and so on. Number Number of Correct Students (5 points) Compute the sample mean number correct. 2. (5 points) Compute the sample standard deviation.

6 6 7. (10 points) The following table summarizes results on an ELISA test used to aid in diagnosing Anthrax. These results are based on tests performed on 12 anthrax cases, and 18 persons who did not have Anthrax. Use this table to answer the following questions. ELISA for poly-d-glutamic acid capsule Anthrax Case No Anthrax Total Test Positive Test Negative Total a. (2 points) What is the sensitivity of the test? b. (2 points) What is the specificity of the test? c. (3 points) Anthrax is relatively rare in the US population. Assume that the prevalence of Anthrax is 1 in 1,000,000. Now, suppose a simple random sample of 1,000,000 people are tested for Anthrax. Among the 1,000,000 people tested, what proportion would you expect to have positive test results? d. (3 points) How many false positive results would you expect as a result of the 1,000,000 tests?

7 7 8. (10 points) The following is a frequency table summarizing survival times of 347 patients newly diagnosed with cancer. Survival Time, years Frequency Cumulative Frequency < at least a. (3 points) What is the most frequently occurring survival time? b. (3 points) 50% of the cohort survive at least. c. (2 points) Is it possible to calculate the average survival time? Explain. d. (2 points) Is the distribution of survival times symmetric or asymmetric? Explain.

8 8 9. (10 points) The following are three histograms: a. (3 points) Is the average indicated by histogram a closest in value to 25, 40, 50, 60, or 75? b. (2 points) Is the average indicated by histogram b closest in value to 25, 40, 50, 60, or 75? c. (2 points) Is the average indicated by histogram c closest in value to 25, 40, 50, 60, or 75? d. (3 points) In your opinion, which of the following two statements is correct? Explain. (i) (ii) The average age of undergraduate students in the United States is larger than the median age of undergraduate students. The average age of undergraduate students in the United States is smaller than the median age of undergraduate students.