Final Exam Terms

Question 1

When are sample proportions normally distributed (i.e. what assumptions must be met?)

Answer 1

np >= 10

n(1 - p) >= 10

Question 2

The sample proportions might NOT follow a normal distribution if …

Answer 2

1. p is close to 0 or 1
2. small n

Question 3

When do we use two-sided or one-sided tests?

Answer 3

When the sign of Ha is does not equal, use both tails ( p x 2)

If Ha is < or >, use one tail to compute p

Question 4

What assumptions must be met for a one proportion CI?

Answer 4

nphat >= 10

n(1 - phat) >= 10

Question 5

How do we calculate a sample size for a one proportion test?

Answer 5

n = (z*/ME)^2 (p squiggle)(1 - p squiggle)

p squiggle is an estimate for the proportion

ALWAYS ROUND UP

Question 6

What is p~ ( p squiggle)

Answer 6

it is the estimated proportion

If not provided p squiggle is 0.5

Question 7

How is a hypothesis test set up for a two proportion test?

Answer 7

H0: p1 = p2
Ha: p1 does not equal p2

Question 8

How do you interpret the confidence interval of a two proportion test?

Answer 8

We are __% confident that the difference in the population proportions of (insert variables) is between ___ and ____.

Question 9

How do you set up a hypothesis test for a chi square test?

Answer 9

H0: p1 = p2 = p3 ….
Ha: some p does not equal some value

Question 10

What is the formula for chi square goodness of fit test?

Answer 10

X(chi)^2 = the sum of (observed - expected)^2/expected

Question 11

In a chi square test, what is the formula for expected counts?

Answer 11

n(p sub i)

pi is given in the null hypothesis

Question 12

When do we use a t distribution?

Answer 12

1 or 2 paired means

Question 13

When do we use a z distribution?

Answer 13

1 or 2 proportions

Question 14

When do we use a chi square distribution?

Answer 14

When we have more than 2 proportions

Question 15

How does a chi-square distribution appear? (i.e. what shape?)

Answer 15

right skewed

Question 16

What happens to a chi-square distribution as df increases?

Answer 16

The degree of skew decreases and approaches a normal distribution.

Question 17

What assumptions must be met for chi-square distribution?

Answer 17

each of the expected counts must be >= 5

Question 18

What tail test do we use for finding p-value with a chi-square test?

Answer 18

always the right tail

Question 19

What chi-square test do we use for two categorical variables?

Answer 19

chi square test for association

(goodness of fit for one categorical variable)

Question 20

How do we set up a hypothesis test for a chi square test for association?

Answer 20

H0: variable A is not associated with variable B
Ha: variable A is associated with variable B

Question 21

How do we calculate expected counts for chi-square test of association?

Answer 21

expected count = (row total x column total)/sample size (n)

Question 22

How do we calculate degrees of freedom for chi-square tests?

Answer 22

goodness of fit: df = k -1

association: df = (r - 1)(c - 1)

Question 23

How do we graph two quantitative variables?

Answer 23

scatterplot

Question 24

What does correlation do?

Answer 24

Measures the strength and direction of a linear relationship between two quantitative variables.

Question 25

How do we describe correlation in terms of paramaters and statistics?

Answer 25

paramater: rho

statistic: r aka correlation coefficient

Question 26

What is the correlation coefficient range?

Answer 26

the smallest r can be is -1, the largest it can be is 1

Question 27

What does it mean if r is positive?

Answer 27

as one variable increases, the other variable increases

direct/positive relationship

Question 28

What does it mean if r is negative?

Answer 28

as one variable increases, the other variable decreases

inverse relationship

Question 29

What does it mean if r is 0?

Answer 29

There is no linear relationship

Question 30

The farther r is away from zero …

Answer 30

The stronger the linear relationship

(min -1, max +1)

Question 31

How do you set up a correlation hypothesis test?

Answer 31

H0: rho = 0
(no linear relationship, variables are not correlated)

Ha: rho does not equal 0
(linear relationship, variables are correlated)

Question 32

Does correlation imply causation?

Answer 32

Not always, must consider if an experiment is observational or experimental, or if there are any confounding variables

Question 33

Is r resistant to outliers?

Answer 33

no

Question 34

What does linear regression do?

Answer 34

Uses one quantitative variable to predict changes in another quantitative variable.

or using an explanatory variable to predict changes in the response variable

Question 35

What is the linear regression equation?

Answer 35

y hat = a + bx

y hat: predicted response value
a = y intercept; predicted value of y when x = 0
b = slope; change in y for one unit change in x

Question 36

What is the difference between simple and multiple linear regression.

Answer 36

simple has one explanatory variable

multiple has two or more explanatory variables

Question 37

How is the residual calculated?

Answer 37

residual = actual y - predicted y

or = y - y hat

Question 38

What does it mean if the residual is positive or negative?

Answer 38

positive residuals are above the line of best fit

negative residuals are below the line of best fit

Question 39

What is ANOVA?

Answer 39

analysis of variance; helps determine if there is a difference between two or more means

Question 40

For ANOVA, what are the factor and response

Answer 40

factor is the x variable, a categorical variable

response is the y variable, a quantitative variable

Question 41

How is the hypothesis test set up for ANOVA?

Answer 41

H0: mu1 = mu2 = mu3 …
Ha: at least one mu does not equal another mu

Question 42

How is df error found?

Answer 42

Df total (calculated as normal, n - 1) - Df factor (#groups - 1)

Question 43

Describe F-distributions

Answer 43

F-distributions are right skewed, must use a right tail test when using the F-statistic to find the p value

Question 44

How do you interpret a Tukey Comparison?

Answer 44

They ensure that the Type-1 error rate is not inflated.

As long as the data spread is not overlapping 0, the means are different.