Unit 5

Question 1

What is the purpose of descriptive statistics?

Answer 1

they provide conclusions about a sample, such as position, central tendency, and variability. They summarize the data for easier interpretation

Question 2

What is the purpose of inferential statistics?

Answer 2

they provide conclusions about the population. They use sample data to make generalizations or predictions about a larger group

Question 3

What is the difference between statistics and parameters?

Answer 3

Statistics (^ø) are estimated based on a sample
Parameters (ø) are values that describe the entire population
-> statistics are used as estimators of parameters

Question 4

What is the role of probability theory in statistics?

Answer 4

It is the foundation for inferential statistics.
-> helps estimate the likelihood of obtaining specific results and assists in making conclusions based on random or deterministic phenomena

Question 5

What is a conceptual hypothesis?

Answer 5

a broad statement predicting a relationship between two variables
-> e.g.: “Class attendance is related to academic performance.” It guides the research and sets the foundation for further testing

Question 6

What is an operative (statistical) hypothesis?

Answer 6

a specific, testable prediction that can be confirmed or refuted with data.
-> e.g.: “The average grade of students with more than 60% attendance will be higher than that of students with less than 60% attendance.” (H: μ1 > μ2)

Question 7

What does the hypothesis “H: µ1 > µ2” represent in this hypothesis: The average grade of students with more than 60% attendance will be higher than that of students with less than 60% attendance

Answer 7

it predicts that the average grade of students with more than 60% attendance (μ1) will be higher than the average grade of students with less than 60% attendance (μ2)

Question 8

What is the conceptual hypothesis?

Answer 8

it is a direct statement and easy to understand

Question 9

what is the operational hypothesis?

Answer 9

quantifiable, measurable and ultimately analyzable terms
-> inform how the concepts or variables will be measured
-> is about quantifying, to be able to compare and verify the stated relationship in an objective way

Question 10

in what terms do we use statistical hypothesis?

Answer 10

in terms of statistics or parameters

Question 11

What are statistical hypotheses formulated with?

Answer 11

the population in mind, not the sample

Question 12

What is the purpose of an operative/statistical hypothesis?

Answer 12

An operative/statistical hypothesis is used to quantify and compare the stated relationship in an objective way, allowing for verification of the claim

Question 13

What is the null hypothesis (H0)?

Answer 13

it always states equality, meaning there is no effect, difference, or association. It assumes no relationship between variables.
-> e.g.: “There is no effect, the difference is 0.

Question 14

What is the alternative hypothesis (H1)?

Answer 14

it is the opposite of the null hypothesis. It states that there is an effect, difference, or association. It is based on the research hypothesis.
-> e.g.: “The effect is not equal to 0 (Effect ≠ 0)

Question 15

How do we test hypotheses?

Answer 15

by checking whether our claim can be supported by evidence from the population. We compare the null hypothesis (H₀) with the alternative hypothesis (H₁) using data

Question 16

What does a directional hypothesis predict?

Answer 16

it predicts a particular direction of difference between population

Question 17

What is an example for Directional hypothesis regarding this hypothesis: The air-conditioned (AC) group will get better final marks than the non-air-conditioned (SA) group

Answer 17

H0: 𝜇AC ≤ 𝜇SA
H1: 𝜇AC > 𝜇SA

Question 18

What is an example for Nondirectional hypothesis regarding this hypothesis: Extroverted people will show different mean self-esteem scores than introverted people

Answer 18

H0: 𝜇E = 𝜇I
H1: 𝜇E ≠ 𝜇I

Question 19

What does a Nondirectional hypothesis predict?

Answer 19

It does not predict a particular direction of difference

Question 20

Do a hypothesis testing for this:
Operational hypothesis: University students who experience high levels of academic stress show a worse academic performance compared to those with low levels of stress.

Answer 20

It is..
Directional (One-tailed)
H1: µHS < µLS
H0: µHS ≥ µLS

Question 21

How are directional and nondirectional hypotheses tested in inferential statistics?

Answer 21

Directional and nondirectional hypotheses are tested using the same general process, but the predictions differ:

Directional hypothesis: Predicts a specific direction of the difference.
Nondirectional hypothesis: Does not predict a specific direction of the difference

Question 22

How is a hypothesis tested in inferential statistics?

Answer 22

statistics rely on probabilities to determine the likelihood of a certain effect, assuming the null hypothesis is true.
-> helps us assess if the evidence supports the alternative hypothesis

Question 23

What does the probability in hypothesis testing represent?

Answer 23

how likely it is that a certain effect will occur, assuming the null hypothesis is true.
-> helps determine whether the observed data is consistent with the null hypothesis

Question 24

Why do we use samples and statistics to test hypotheses?

Answer 24

to test hypotheses and generalize the results to the population, as it’s often impractical to test the entire population

Question 25

How is a statistic from a sample related to a population?

Answer 25

it is analogous to a direct score from the population, but with the limitation that it might not be identical due to measurement error

Question 26

Why do different samples show different statistics?

Answer 26

due to measurement error

Question 27

What is assumed about the distribution of scores and statistics?

Answer 27

that scores and statistics follow a certain distribution, typically the normal distribution, which is key for hypothesis testing

Question 28

What does the Central Limit Theorem state?

Answer 28

if a random variable (X) is normally distributed in the population, and we take infinite random samples of size N and calculate their means, the resulting distribution of sample means will approximate a normal distribution

Question 29

When can we predict probabilities?

Answer 29

if the variable’s distribution is normal

Question 30

What are Parametric tests?

Answer 30

those that make assumptions about the parameters of the population
distribution from which the sample is drawn
-> This is often the assumption that the population data are normally distributed

Question 31

What Non-parametric tests?

Answer 31

they are “distribution-free” and, as such, can be used for non-normal variables.

Question 32

What is the formula to calculate a Z-Score for a sample mean?

Answer 32

z = (ˉx - µ) : (σ:√n)

Question 33

What is the p-value?

Answer 33

Probability associated to the statistics.
How likely is to find that statistic by chance
-> if probability is really low, probability of H0 being true is reduced

Question 34

When do we accept or reject H0 and H1?

Answer 34

p ≤ 𝛂
p ≤ 0.05 = Reject H0, Accept H1

p > 𝛂
p > 0.05 = Accept H0, Reject H1

Question 35

What is a two-tailed (nondirectional) hypothesis test, and how is it represented?

Answer 35

A two-tailed (nondirectional) hypothesis test tests for the possibility of an effect in two directions (either positive or negative). The alternative hypothesis (H1) does not predict a direction, just that there is a difference
- Null Hypothesis (H₀): 𝜇 = μ0
(Population mean equals a specific value)
- Alternative Hypothesis (H1): µ ≠ µ0
(Population mean is not equal to the specified value)

Question 36

What is a left-tailed (directional) hypothesis test, and how is it represented?

Answer 36

A left-tailed (directional) hypothesis test tests whether the sample mean is significantly less than the population mean.

• Null Hypothesis (H₀): µ ≥ µ0
  (Population mean is greater than or equal to a specified value)
• Alternative Hypothesis (H₁): µ < µ0
  ​(Population mean is less than the specified value)

Question 37

What is a right-tailed (directional) hypothesis test, and how is it represented?

Answer 37

A right-tailed (directional) hypothesis test tests whether the sample mean is significantly greater than the population mean.

• Null Hypothesis (H₀): µ ≤ µ0
  (Population mean is less than or equal to a specified value)
• Alternative Hypothesis (H₁): µ > µ0
  ​(Population mean is greater than the specified value)

Question 38

What are the statistical decisions made when performing a hypothesis test?

Answer 38

• The null hypothesis (H0) is either accepted or rejected based on the results of the test.
• If the p-value is less than the significance level (α), the null hypothesis is rejected.
• If the p-value is greater than the significance level (α), the null hypothesis is not rejected (it is accepted).

Question 39

What are right decisions in Type I and Type II Errors?

Answer 39

• The null hypothesis (H0) is true and it is accepted.
• The null hypothesis (H0) is false and it is rejected.

Question 40

What are wrong decisions in Type I and Type II Errors?

Answer 40

• The null hypothesis (H0) is true and it is rejected.
• The null hypothesis (H0) is false and it is accepted.

Question 41

What is Confidence Interval estimation?

Answer 41

Estimate a range of values (symmetrical with respect to the mean) among
which the true value can be found, with a high and known probability

Question 42

What 2 values are there in confidence interval?

Answer 42

Upper limit (UL)
Lower limit (LL)

Question 43

What is the procedure in Confidence interval?

Answer 43

• find out standard error of statistic
• find the maximum sampling error (Emax)
• find the lower limit, subtract the Emax from the statistic
• find the upper limit, add the Emax to the statistic