LV_Questions

Question 2

*1. The sum of all the probabilities of all possible outcomes of a random event is 1.

Answer 2

True

Question 3

*2. A 95% confidence interval is an interval that covers 95% of the data.

Answer 3

False

Question 4

*3. If two events are independent in a statistical sense, the probability of both events occurring is always the sum of the individual probabilities.

Answer 4

False

Question 5

*4. The p-value of a statistical test represents the type II error, which is defined as the probability of a false test result.

Answer 5

False

Question 6

*5. If the mean, the median, and the mode of a data set are identical, the data is always skewed.

Answer 6

False

Question 7

*6. A Bravais-Pearson correlation coefficient of 0 indicates a perfect linear relationship, as there is 0 deviation between the two variables.

Answer 7

False

Question 8

*7. The interquartile range (IQR) is defined as the sum of the first quartile and the third quartile.

Answer 8

False

Question 9

*8. Given, a continuous random variable X has the probability density function $f(x)$. The probability that X takes on a value in the interval [a,b] is given by $f(b)-f(a)$.

Answer 9

False

Question 10

*9. The a-priori probability in Bayes’ theorem represents the conditional probability of an event given that another event has already occurred.

Answer 10

False

Question 11

*10. The central limit theorem states that the variance of a sample increases as the sample size also increases.

Answer 11

False

Question 12

*11. A box plot is a graphic usually used to visualize the mode of a data set.

Answer 12

False

Question 13

*12. If two events A and B are independent, then $P(A\cap B)$ is defined as $P(A)/P(B)$.

Answer 13

False

Question 14

*13. A histogram is used to analyze the relationship between two variables.

Answer 14

False

Question 15

*14. The mean, as a measure of central tendency, is not affected by extreme values in the data set.

Answer 15

False

Question 16

*15. In simple linear regression, the line of best fit $(=$ regression line) is determined by minimizing the sum of the squared median deviation.

Answer 16

False

Question 17

*16. If two events A and B are mutually exclusive, then $P(A\cup B)$ is defined as $P(A)/P(B)$.

Answer 17

False

Question 18

*17. The sample standard deviation is always smaller than the population standard deviation.

Answer 18

False

Question 19

*18. The so-called ‘critical value’ of a statistical test is just the value of the test statistic of this statistical test.

Answer 19

False

Question 20

*19. If X and Y are continuous random variables with the joint probability density function $fxy(x.y)$. The conditional probability density function $f(x|y)$ is defined as $fxy(x,y)/fy(x)$.

Answer 20

False

Question 21

*20. The statement $P(A\cup B)=P(A)+P(B)-P(A\cap B)$ is true for non-disjoint events.

Answer 21

True

Question 22

Statistics is primarily concerned with collecting, organizing, presenting, and interpreting numerical facts.

Answer 22

True

Question 23

Descriptive statistics aims to generalize conclusions from a sample to an unknown population.

Answer 23

False

Question 24

Inductive statistics uses probability theory to draw conclusions about a population from a sample.

Answer 24

True

Question 25

A statistical model is a system of assumptions and equations describing data, but not suitable for prediction.

Answer 25

False

Question 26

A poll of internet users, while large, constitutes a scientific poll for determining public opinion.

Answer 26

False

Question 27

Scientific facts are determined by public opinion polls.

Answer 27

False

Question 28

If two poll numbers differ by less than the margin of error, it is always a significant news story.

Answer 28

False

Question 29

In an inverted chart, the information is represented by the white area under the curve.

Answer 29

False

Question 30

Qualitative data always has a meaningful order.

Answer 30

False

Question 31

Ordinal data allows for meaningful ranking and ordering, but not quantifiable distances between values.

Answer 31

True

Question 32

The interval scale of measurement has an objectively defined zero point.

Answer 32

False

Question 33

Ratio data allows for all arithmetic operations (addition, subtraction, multiplication, division).

Answer 33

True

Question 34

Gender is an example of ordinal data.

Answer 34

False

Question 35

The number of carious teeth of school children is an example of quantitative-continuous data.

Answer 35

False

Question 36

Stock data is measured over an interval of time.

Answer 36

False

Question 37

Extensive data yields useful information when averaged, but not when summed up.

Answer 37

False

Question 38

*A quantitative-discrete attribute can be counted.

Answer 38

"True"

Question 39

*Quantitative-continuous attributes can be measured with infinite precision.

Answer 39

"True"

Question 40

*A Type I error occurs when an experiment finds no difference, but there is a difference in the population.

Answer 40

"False"

Question 41

*A Type II error means that an experiment finds a difference when there is no difference in the population.

Answer 41

"False"

Question 42

*The Central Limit Theorem states that if your sample size is large enough (e.g., >30), the sample mean distribution will converge to a normal distribution.

Answer 42

"True"

Question 43

*The Bravais-Pearson correlation coefficient has a range from $-\infty$ to $+\infty$.

Answer 43

"False"

Question 44

*The statement $P(A \cap B) = P(A) * P(B)$ holds for any event without any restrictions.

Answer 44

"False"

Question 45

*Given a continuous random variable, the probability density function $f(x)$ is exactly the probability that the random variable is $x$.

Answer 45

"False"

Question 46

*The variance has a range from $0$ to $\infty$.

Answer 46

"True"

Question 47

*The normal distribution plays an important role in inductive statistics because of the Central Limit Theorem and its prevalence in natural phenomena.

Answer 47

"True"

Question 48

*The p-value is the probability under the null hypothesis of obtaining a result as extreme as, or more extreme than, the observed result.

Answer 48

"True"

Question 49

*If the p-value is small, the null hypothesis is typically not rejected.

Answer 49

"False"

Question 50

*Metric-discrete data consists of values from a fixed list of numbers.

Answer 50

"True"

Question 51

*Metric-continuous data can be determined with infinite precision.

Answer 51

"True"

Question 52

*The arithmetic mean is always stable against great outliers in the data.

Answer 52

"False"

Question 53

*The mode (modal value) must always be unique.

Answer 53

"False"

Question 54

*The covariance has a range from $0$ to $+\infty$.

Answer 54

"False"

Question 55

*The standard error is completely independent from the sample size.

Answer 55

"False"

Question 56

*The median is an appropriate measure of location for ordinal data.

Answer 56

"True"

Question 57

*For nominal data, the mean is an appropriate summary statistic.

Answer 57

"False"

Question 58

*If the sample size is increased while keeping the confidence level constant, the precision of the confidence interval decreases.

Answer 58

"False"

Question 59

*Inductive statistics aims to draw conclusions from a sample and generalize them to a population.

Answer 59

"True"

Question 60

*The Spearman rank correlation coefficient should be used instead of the Bravais-Pearson correlation coefficient if the bivariate data is ordinal or contains outliers.

Answer 60

"True"

Question 61

*The sum of all the probabilities of all possible outcomes of a random event is 1.

Answer 61

"True"

Question 62

*A 95% confidence interval is an interval that covers 95% of the data.

Answer 62

"False"

Question 63

*If two events are independent in a statistical sense, the probability of both events occurring is always the sum of the individual probabilities.

Answer 63

"False"

Question 64

*The p-value of a statistical test represents the type II error.

Answer 64

"False"

Question 65

*If the mean, the median, and the mode of a data set are identical, the data is always skewed.

Answer 65

"False"

Question 66

*A Bravais-Pearson correlation coefficient of 0 indicates a perfect linear relationship.

Answer 66

"False"

Question 67

*The interquartile range (IQR) is defined as the sum of the first quartile and the third quartile.

Answer 67

"False"

Question 68

*Given a continuous random variable X with probability density function $f(x)$, the probability that X takes on a value in the interval $[a,b]$ is given by $f(b)-f(a)$.

Answer 68

"False"

Question 69

*The a-priori probability in Bayes' theorem represents the conditional probability of an event given that another event has already occurred.

Answer 69

"False"

Question 70

*The central limit theorem states that the variance of a sample increases as the sample size also increases.

Answer 70

"False"

Question 71

*A box plot is a graphic usually used to visualize the mode of a data set.

Answer 71

"False"

Question 72

*If two events A and B are independent, then $P(A \cap B)$ is defined as $P(A)/P(B)$.

Answer 72

"False"

Question 73

*A histogram is used to analyze the relationship between two variables.

Answer 73

"False"

Question 74

*The mean, as a measure of central tendency, is not affected by extreme values in the data set.

Answer 74

"False"

Question 75

*In simple linear regression, the line of best fit (regression line) is determined by minimizing the sum of the squared median deviation.

Answer 75

"False"

Question 76

*If two events A and B are mutually exclusive, then $P(A \cup B)$ is defined as $P(A) * P(B)$.

Answer 76

"False"

Question 77

*The sample standard deviation is always smaller than the population standard deviation.

Answer 77

"False"

Question 78

*The so-called 'critical value' of a statistical test is just the value of the test statistic of this statistical test.

Answer 78

"False"

Question 79

*If X and Y are continuous random variables with the joint probability density function $f_{xy}(x,y)$, the conditional probability density function $f_{x|y}(x|y)$ is defined as $f_{xy}(x,y)/f_x(x)$.

Answer 79

"False"

Question 80

*The statement $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ is true for non-disjoint events.

Answer 80

"True"

Question 81

*In the case of two disjoint events A and B, the intersection of these two events ($A \cap B$) is always the empty set.

Answer 81

"True"

Question 82

*The statement $P(A \cup B) = P(A) + P(B)$ holds for any kind of probability events.

Answer 82

"False"

Question 83

*The statement $P(A) * P(B) = P(A \cap B)$ holds for any kind of probability events.

Answer 83

"False"

Question 84

*The expression $P(A \setminus B)$ is just another notation for $P(A) - P(A \cap B)$.

Answer 84

"True"

Question 85

*The a-priori probability is always equal to the posteriori probability.

Answer 85

"False"

Question 86

*An empirical cumulative distribution can be presented in some special case by a monotonic decreasing function.

Answer 86

"False"

Question 87

*A bar plot is always an optimal way to present information about metric-continuous data.

Answer 87

"False"

Question 88

*In case of metric-discrete data the empirical distribution function is a step-function.

Answer 88

"True"