Statistics I

Question 1

Define Measurement!

Answer 1

The process of assigning a number to an attribute (or phenomenon) according to a (set of) rule(s).

Question 2

Define Sample!

Answer 2

A collection of individual observations selected by a specific procedure.

Question 3

Define Population!

Answer 3

Totality of individual observations about which inferences are to be made.

Question 4

What’s a variable?

Answer 4

A symbol that stands for a value that may vary.

Question 5

Statistics dealing with just one variable is called?

Answer 5

Univariate Statistics

Question 6

Who introduced the student’s t-test? and when?

Answer 6

William Seal Gosset, 1908

Question 7

What is Hotelling’s t-squared test in comparison to the student’s t-test?

Answer 7

Hotelling’s t-squared test is the multivariate extension to the t-test.

Question 8

What’s the Type I error?

Answer 8

We reject H0, but it is true.

Question 9

What’s the Type II error?

Answer 9

We accept H0, but it is false.

Question 10

What does H0 stand for?

Answer 10

Null-Hypothesis

Question 11

What’s the p-value dealing with H0?

Answer 11

Probability of a Type I error.

Question 12

How is the Student’s t-test defined on wikipedia?

Answer 12

A two-sample location test of the null hypothesis that the means of two normally distributed populations are equal.

Question 13

The name “Student’s t-test” should strictly speaking only be applied, if …

Answer 13

… the variances of the two tested populations are also assumed to be equal.

Question 14

A “Student’s t-test” in which the variances of the two populations are not hypothesized to be equal is sometimes called …

Answer 14

… Welch’s t-test.

Question 15

What is a dependent variable?

Answer 15

The dependent variable represents the output or effect, or is tested to see if it is the effect.

Question 16

What is an independent variable?

Answer 16

The independent variables represent the inputs or causes, or are tested to see if they are the cause.

Question 17

Roles of dependent and independent variables in statistics:

Answer 17

In a statistical experiment, the dependent variable is the event studied and expected to change, whenever the independent variable is altered.

Question 18

In a study whether taking vitamin C pills daily make people live longer, researchers will dictate the vitamin C intake of a group of people over time. One part of the group will be given vitamin C pills daily. The other part of the group will be given a placebo pill. Nobody in the group knows which part they are in. The researchers will check the life span of the people in both groups. Idependent and dependent variables?

Answer 18

Here, the dependent variable is the life span and the independent variable is a binary variable for the use or non-use of vitamin C.

Question 19

In a study measuring the influence of different quantities of fertilizer on plant growth,
the independent variable would be …
The dependent variable would be …
The controlled variables would be …

Answer 19

… the amount of fertilizer used.
…the growth in height or mass of the plant.
… the type of plant, the type of fertilizer, the amount of sunlight the plant gets, the size of the pots, etc.

Question 20

In a study of how different doses of a drug affect the severity of symptoms, a researcher could compare the frequency and intensity of symptoms when different doses are administered.
Idependent and dependent variables?

Answer 20

Here the independent variable is the dose and the dependent variable is the frequency/intensity of symptoms.

Question 21

In measuring the amount of color removed from beetroot samples at different temperatures, temperature is …
and amount of pigment removed is …

Answer 21

… the independent variable …

… the dependent variable.

Question 22

In sociology, in measuring the effect of education on income or wealth, the dependent variable is …
and the independent variable is …

Answer 22

… level of income/wealth …

… the education level of the individual.

Question 23

What’s variance?

Answer 23

a quantity equal to the square of the standard deviation.

Question 24

What’s standard deviation?

Answer 24

A quantity calculated to indicate the extent of deviation for a group as a whole.

Question 25

What is the median?

Answer 25

The value so that half of the values are above it and half of them are below it.
e.g. 56, 75, 84, 265, 266 -> median = 84

Question 26

What’s the “mode”?

Answer 26

the value that occurs most often
e.g. 1, 3, 2, 2, 3, 3, 3, 4, 3
mode = 3

Question 27

2, 2, 3, 4, 10
mean?
median?
mode?

Answer 27

2, 2, 3, 4, 10
mean = 4.2
median = 3
mode = 2

Question 28

List three statistical measures of dispersion!

Answer 28

• Range
• Variance
• Standard Deviation

Question 29

Another term for variance?

Answer 29

mean squared deviation

Question 30

A measure to represent the asymmetry of data?

Answer 30

Skewness

Question 31

two possible Skewness values?

Answer 31

Right skewed (e.g. distribution of wealth)
Left skewed (on what side is the long tail?)

For a unimodal distribution, negative skew indicates that the tail on the left side of the probability density function is longer or fatter than the right side – it does not distinguish these shapes. Conversely, positive skew indicates that the tail on the right side is longer or fatter than the left side.