STATISTICS- MCQ/EXCLUSIVES

STATISTICS/MCQ:

Q. Given the following collection of data {1,2,4,6,7,8,9}, which is correct?
A. The mean is 5.0.
B. The median is 5.0.
C. The median is 5.5.
D. The median is 6.0.
E. The mean is 6.0.

Ans:. D.

 Given the set of numbers {1,2,4,6,7,8,9}, the sum of these numbers is 37 and there are seven values, so the mean is 37/7 =5and2/7, or 5.28. The median, which is the center of an odd number of values, is the number 6, with 1, 2, and 4 below and 7, 8, and 9 above. 

Q. Given the following collection of data {1,1,1,1,2,3,5,5, 6,6,7,7,9,9}, which of the following is correct?
A. The mode is 1.
B. The mean is 4.5.
C. The median is 6.
D. A and B are correct.
E. A and C are correct

Ans. D.

Given the set of numbers {1,1,1,1,2,3,5,5,6,6,7,7,9,9}, there are 14 numbers, and their sum is 63. Thus the mean is 4.5; clearly, the median is 5; and the mode is 1. Thus, the answer is (D), which is a mode of 1 and a mean of 4.5.

Q. You are told that your patient has a cholesterol result that is the mean of that in the population. Which of the following distributions would also mean that his result is necessarily
greater than half of the population?
A. Skewed to the left
B. Skewed to the right
C. Uniform
D. Normal
E. Bimodal

Ans:  B.

The question asks, “In what type of distribution is the mean greater than the median?”The mean will equal the median in normal and uniform distributions. In a symmetric bimodal distribution this will also be true. In a skewed-to-the-left distribution, the median will be greater than the mean, whereas in a skewed-tothe- right distribution, the mean will be greater than the median.

Q. You are designing a study to investigate whether ethnicity is associated with hypertension. You have a cohort of 500 patients of Asian, African , Indian, American ethnicity. Which of the following tests would be the best to compare the results of the study?
A. Student t test
B. Power analysis
C. z test
D. Chi-square test
E. Bonferroni correction

Ans. D.

 In this study design, you are attempting to determine whether there is a difference in any of these groups of patients with respect to the risk for type 2 diabetes. The test that is needed must be able to compare proportions between multiple groups. The only one that can do that is the chi-square test. The student t test is to compare two means; the z test is to compare the proportions of two groups. A power analysis is performed to measure the power of a particular study to reject the null hypothesis. A Bonferroni correction is performed when making more than one comparison, using, for example, a student t test. Using a cutoff of the test that allows a 5% chance of type I error goes awry when you make many comparisons of outcomes in the same study. For example, if you compared 100 different means, on average you would expect five of them to meet the p _ .05 requirement. Thus, a Bonferroni or, more commonly, the student- Newman-Keuls test can be used to adjust the cutoff when making multiple comparisons.

Q. Which of the following best describes a type I error?
A. There is a positive result on a screening test, but the patient does not have the disease.
B. There is a positive result on a screening test, and the patient does have the disease.
C. There is a negative result on a screening test, and the patient does not have the disease.
D. There is a negative result on a screening test, but the patient does have the disease.
E. None of the above

Ans: E.

Type I error is that of having a false-positive result. So type I error equals the number of false-positive results over the total number of patients with true results that are negative or not diseased. Type II error is the false-negative mistake. Thus, type II error equals the number of false negatives over the total number of patients with disease, or with true results that are positive