Lecture 5 REVISED

Question 1

distribution = ?

Answer 1

a collection of data/scores

Question 2

how are the values of a distribution ordered?

Answer 2

commonly ordered (e.g., smallest to largest)

Question 3

steps to building a discrete probability distribution

Answer 3

1. define the random variable
2. identify values for the random variable
3. assign probabilities to values of the random variable

Question 4

what are the two general requirements for discrete distributions?

Answer 4

every probability is greater than or equal to 0

the sum of all probabilities must equal 1

Question 5

how to calculate expected value/mean of a random variable?

Answer 5

multiply every variable by their probability and then sum up all the outcomes

Question 6

how to calculate the variance of a random variable?

Answer 6

• subtract the data point from the mean
• square the difference
• multiply the difference by the probability
• sum up all the squared deviations*probabilities

Question 7

normal distribution

Answer 7

most popular distribution

represents many natural phenomena

bell shaped, relatively symmetrical curve

Question 8

what is the highest point on a normal distribution curve?

Answer 8

the mean (which is also the mode & median)

Question 9

what is standard normal distribution?

Answer 9

special normal distribution with a mean of 0 and a standard deviation of 1

standard normal distribution is centred at 0 and has intervals that increase by 1

each number on horizontal axis is a z-score

Question 10

what do z-scores tell us?

Answer 10

tells us how many standard deviations a data point is from the mean

e.g., z-score -2 is 2 standard deviations to the left of the mean 0

Question 11

what does a z-score table tell us?

Answer 11

tells us the total amount of area contained to the left of z

Question 12

how do you calculate the area to the right of z?

Answer 12

1- area that corresponds to z value

e.g., z = 0.57, 0.7157 area to the left, 1-0.7157=0.2843 area to the right

Question 13

how do you calculate z-scores for a normal distribution?

Answer 13

z = (x-mean)/standard deviation

Question 14

two ways standard normal distribution can be used?

Answer 14

forward - from x, calculate z & find the probability/area associated with z

reverse - from probability/area, find z and calculate the data value x associated with that area

Question 15

rule 68-95-99.7 / empirical rule?

Answer 15

used to remember the percentage of values that lie within an interval

only refers to normal distribution

68.3% of data falls within 1 standard deviation of the mean

95% of the data falls within 2 standard deviations of the mean

99.7% of the data falls within 3 standard deviations of the mean

Question 16

central limit theorem (CLT)?

Answer 16

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

Question 17

law of large numbers (LLN)?

Answer 17

n > 30 is considered a ‘large’ sample size

when an action is repeatedly performed, the outcome eventually approaches the expected outcome (mean)

Question 18

hypothesis = ?

Answer 18

a statement made about a characteristic of a particular populationt

Question 19

two types of hypotheses?

Answer 19

null hypothesis - statement made, to be tested (H0)

alternative hypothesis - opposite to the null hypothesis (Ha)

Question 20

status quo = ?

Answer 20

null hypothesis

Question 21

what is a one/two tailed test?

Answer 21

one tailed = testing one end of the dataset

two tailed= creating a hypothesis about both ends of the dataset, non-directional

Question 22

right/left tailed test?

Answer 22

right tailed = hypothesis testing the upper end of the dataset

left tailed test = hypothesis testing the lower end of the dataset

Question 23

significance level?

Answer 23

when testing a hypothesis, there’s a limit/threshold that defines whether or not the hypothesis is true

(alpha) usually 0.05 (5%)

Question 24

failure to reject a null hypothesis?

Answer 24

no proof that null hypothesis isn’t true, but isn’t certain that it IS true