Lecture 5

Question 1

distribution = ?

Answer 1

a distribution is a collection of data/scores of a variable

Question 2

how are the values of a distribution ordered?

Answer 2

values of a distribution are commonly ordered

(e.g., from smallest to largest)

Question 3

probability distribution = ?

Answer 3

a mathematical function that calculates the probability of possible outcomes

Question 4

how is a discrete probability distribution portrayed?

Answer 4

breaks/holes between values

probability is represented by the height of each bar (on bar chart)

Question 5

how is a continuous probability distribution portrayed?

Answer 5

in a continuous probability distribution, it’s the area instead of the height, that represents the probability

probability is represented by the area under the curve

Question 6

normal distribution = ?

Answer 6

a bell shaped curve, centred in the middle

normal probability distribution is very common in statistical analyses

Question 7

what does skewness measure?

Answer 7

the degree to which a dataset leans

asymmetric distribution of variables

Question 8

gaussian distribution = ?

Answer 8

same as normal distribution

Question 9

where is the highest point on the normal curve in normal distribution?

Answer 9

the mean

Question 10

what does the standard deviation determine regarding a curve?

Answer 10

standard deviation determines the width of the curve

larger standard deviation = wider/flatter curve

smaller standard deviation = narrower curve/pointier

Question 11

how does a normal curve look?

Answer 11

symmetric, bell-shaped

Question 12

standard normal distribution = ?

Answer 12

instead of using units, scores are used as variables

Question 13

z-score = ?

Answer 13

the number of standard deviations from the mean for a particular data point

Question 14

how is z-score for a normal distribution calculated?

Answer 14

(variable - mean) / standard deviation

Question 15

what are the two ways the standard normal distribution is used?

Answer 15

forward and in reverse

forward = for a given data value (x), calculate z and find the probability/area associated with z

reverse = for a given probability/area, find z then calculate the data value x

Question 16

68-95-99.7 / empirical rule = ?

Answer 16

the rule is applied to remember percentage of values that lie within an interval estimate of the normal distribution

rule only works with normal distribution

approximately 68.3% of data will be within 1 standard deviation of the mean

Question 17

central limit theorem (CLT) = ?

Answer 17

as sample size increases, the sampling distribution of the sample mean rapidly approaches the bell shape of a normal distribution

Question 18

what sample size is considered large?

Answer 18

a sample size consisting of more than 30 variables

Question 19

if the population has a normal distribution…

Answer 19

the sampling distribution of the sample mean has a normal distribution for any sample size

according to central limit theorem

Question 20

law of large numbers (LLN) = ?

Answer 20

consists of a theorem that describes the result of performing the same experiment a large number of times

as number of performances increases, the result approaches the expected result (mean/average)

Question 21

hypothesis = ?

Answer 21

a statement regarding the inference of the data

Question 22

how does statistical hypothesis testing work?

Answer 22

• a hypothesis is made about a characteristic of the population
• sample is then taken in an effort to establish whether or not the statement is true
• if sample produced results adverse to the hypothesis, the hypothesis would be considered false

Question 23

what are the two types of hypothesis?

Answer 23

null hypothesis & alternative hypothesis

Question 24

null hypothesis = ?

Answer 24

H0

status quo

the statement to be tested in the hypothesis testing

Question 25

alternative hypothesis = ?

Answer 25

opposite to the null hypothesis

(e.g., the sky is blue on a tuesday = null hypothesis; the sky isn’t blue on a tuesday = alternative hypothesis (Ha)

Question 26

significance level (alpha) = ?

Answer 26

the probability that defines what we mean by unlikely sample results under an assumption that the null hypothesis is true

Question 27

accepting vs failing to reject the null hypothesis = ?

Answer 27

no such thing as accepting a null hypothesis

only failure to reject opposed to accepting the claim