All Minimals

Question 1

What are the permutation of n different elements taken n at a time and what is their number?

Answer 1

Question 2

Define the combinations of n different elements taken k at a time in words.

Answer 2

All possible selections of size k of different elements.

Question 3

Answer 3

Question 4

Define nominal scale and give an example for it.

Answer 4

Question 5

Define ordinal scale and give an example for it.

Answer 5

Question 6

Define interval scale and give an example for it.

Answer 6

Question 7

Define ratio scale and give an example for it.

Answer 7

Question 8

How are the relative frequency and probability of an event related to each other?

Answer 8

Question 9

What is the definition of classical probability?

Answer 9

Question 10

What kind of values can (mathematical) probability assume? What is the probability of a certain and an impossible event?

Answer 10

Question 11

Describe the relationship between the probabilities of event A and its complement event B!

Answer 11

P(A) + P(B) = 1

Question 12

Define the sum of events A and B!

Answer 12

Question 13

What is the probability of the sum of events A and B?

Answer 13

Question 14

Define the product of events A and B!

Answer 14

Question 15

Define the complement event of event A!

Answer 15

Question 16

When are events A and B exclusive?

Answer 16

If AB = 0

Question 17

When are events A and B independent of each other?

Answer 17

Question 18

Using the terms of set theory define:
a. the product of events A and B
b. the sum of events A and B

Answer 18

Question 19

What is the meaning of P(A | B)?

Answer 19

It is a conditional probability of A given B. And the probability of A occurring is dependent on B.

Question 20

What is the definition of a random variable?

Answer 20

Is the number assigned to a random event.

Question 21

What is a continuous random variable?

Answer 21

Question 22

What is the definition of the cumulative relative frequency of a sample?

Answer 22

Question 23

What is the definition of the cumulative distribution function of a random variable?

Answer 23

Question 24

What is the probability that a continuous random variable assumes a value in the interval between a and b?

Answer 24

Question 25

Define the mean of a discrete random variable!

Answer 25

Question 26

Define the variance of a discrete random variable **with a formula**.

Answer 26

Question 27

Define the variance of a sample **with a formula**.

Answer 27

Question 28

Define the variance of a random variable.

Answer 28

Question 29

Define the variance of a sample **in words**.

Answer 29

Question 30

What is the central limit theorem?

Answer 30

Question 31

Define the standard deviation (SD) and the standard error of the mean (SEM) of a sample **with formulas!**

Answer 31

Question 32

What is the difference between the standard deviation (SD) and the standard error of the mean (SEM) of a sample? **Write your answer in words, do not use formulas.**

Answer 32

Question 33

Define the coefficient of variation (CV) in words and with a formula.

Answer 33

Question 34

Define the mean of a sample with a formula and interpret the variables!

Answer 34

Question 35

What is an ordered array?

Answer 35

Question 36

Define the median of a sample!

Answer 36

Question 37

Define the *i*-th percentile of a sample!

Answer 37

Question 38

Define the first, second and third quartile (Q1, Q2, Q3) of a sample.

Answer 38

Question 39

Define the mode of a sample!

Answer 39

Question 40

How can a histogram be constructed?

Answer 40

Question 41

Calculate the mean, median and mode of the data set given below. Data set: 5, 8, 9, 5, 9, 1, 6, 5

Answer 41

Question 42

Calculate the standard deviation and standard error of the mean of the sample given below. Sample: 3, 7, 5

Answer 42

Question 43

Give the *k*th element of a binomial distribution with parameter *p* (the probability of the first possible outcome of a trial) if the total number of trials is *n* (*k* = 0, 1, 2, 3…, *n*), and define the probability it means!

Answer 43

Question 44

Give the *k*th element of a Poisson distribution with parameter λ and define the probability it means!

Answer 44

Question 45

Give the sum of elements of a Poisson distribution with parameter λ!

Answer 45

Question 46

Which two properties of the Poisson distribution are equal to λ, the parameter of the distribution?

Answer 46

Question 47

When does a random variable follow a standard normal distribution?

Answer 47

Question 48

Calculate the standardized *z* value corresponding to a value 135 of a random variable distributed according to a normal distribution with a mean value of 120 and a standard deviation of 10. Calculate the probability that the above random variable will assume a value less than 135.

Answer 48

Question 49

What is the probability that a normally distributed random variable falls in the regions µ +/- 1σ, µ +/- 2σ and µ +/- 3σ (µ is the mean and σ is the standard deviation of the normal distribution)?

Answer 49

Question 50

What is a type I error in a statistical test?

Answer 50

Question 51

What is a type II error in a statistical test?

Answer 51

Question 52

What is the relationship between the probability of committing a type I error and the level of significance?

Answer 52

Question 53

What is the *p* value in hypothesis testing?

Answer 53

Question 54

What is a two-sided statistical test?

Answer 54

Question 55

Write the formula for the statistical test used for single population mean hypothesis testing when the SD of the population is known and interpret the variables!

Answer 55

Question 56

What kind of hypothesis testing can the F test be used for?

Answer 56

Question 57

What kind of quantities can be compared with a two-sample independent groups t-test?

Answer 57

Question 58

When does a statistic give an unbiased estimation of a parameter?

Answer 58

Question 59

When is a sample representative?

Answer 59

Question 60

What are the most important attributes of the quality of an estimate? Define them briefly.

Answer 60

Question 61

Define the null hypothesis for a two-sample, tw-sided (two-tailed) t-test.

Answer 61

Question 62

Write the null hypothesis for an F test.

Answer 62

Question 63

What is the definition of specificity of a clinical diagnostic test?

Answer 63

Question 64

What is the definition of sensitivity of a clinical diagnostic test?

Answer 64

Question 65

What is the definition of positive predictive value?

Answer 65

Question 66

What is the definition of negative predictive value?

Answer 66

Question 67

Draw the 2x2 contingency table characterizing the sensitivity and specificity of a clinical diagnostic test.

Answer 67

Question 68

What is the definition of odds?

Answer 68

Question 69

Define odds ratio from a epidemiological point of view.

Answer 69

Question 70

What is the relative risk in epidemiological studies?

Answer 70

Question 71

Calculate the expected frequency in the upper left cell of the contingency table given below assuming the independence of the two random variables.

Answer 71

Question 72

Specify the X^2 statistic for a test of independence.

Answer 72