skills test 3

Question 1

what is the p value

Answer 1

the probability of getting a result as extreme or more extreme as the observed data if the null hypothesis is true

Question 2

with what p values do we reject or not reject the null hypothesis

Answer 2

if p is larger than alpha - do not reject

if p is less than alpha - reject

if p is low, the null must go

Question 3

how do we work out p values

Answer 3

for a sample mean, t.dist or t.dist.2t

for a sample proportion, norm.s.dist and will have to manipulate and multiply by 2 for 2 tails, use the complement rule, etc

Question 4

what is a type 1 error

Answer 4

when a true null hypothesis is rejected

Question 5

what is a type 2 error

Answer 5

when a false null hypothesis is not rejected

Question 6

why are there errors in hypothesis testing

Answer 6

we never have the whole population to actually know the true population parameter. we never know if we could have just got a particularly unusual sample

Question 7

what is an independent sample

Answer 7

This is where the selection of individuals who make up one sample is independent of the selection of individuals in the other sample.

Eg: an economic wishes to determine whether there is a difference in mean family income for households in 2 socio-economic groups.

Eg: a university wants to compare the mean NCEA results of applicants educated in rural high schools and urban high schools.

Question 8

what is a paired sample

Answer 8

Each observation in one sample can be matched/paired in a meaningful way with a particular observation in the other sample. These are things such as “repeated measurements” or before and after samples.

Eg: Nike wants to see if there is a difference in durability of 2 shoe sole materials. One type is placed on one shoe, the other type on the other shoe of the same pair. In this scenario the same person wears one of each pair.

Eg: An analyst for Educational Testing Service wants to compare the mean test scores of students before and after taking a review course. Each student in the sample is measured twice.

Question 9

The sampling distribution of the difference in sample means can be treated as normal if:

Answer 9

• The original populations are both normal
  
  • If either of the populations is not normally distributed the sample size is large enough (n greater than or equal to 30) for the Central Limit Theorem to apply

Question 10

for stat 101, D0 is always?

Answer 10

0

Question 11

we also use the large sample hypothesis test for?

Answer 11

small sample tests where the variances of those two populations are unequal

Question 12

which degrees of freedom do we use when there are two samples

Answer 12

the smaller of n-1

Question 13

what test do we use to compare variability

Answer 13

F test

Question 14

the F distribution is always __ skewed?

Answer 14

right

Question 15

the test statistic for an F distribution is given by?

Answer 15

larger sample variance/smaller sample variance

Question 16

how do we get df1 and df2 for an F distribution

Answer 16

the numerator of the test statistics sample size - 1 is df1

the denominator of the test statistics sample size - 1 is df2

Question 17

what excel function do we use for the f test using the critical value method

Answer 17

F.INV.RT, divide alpha by 2 for a 2 tailed test

Question 18

what excel function do we use for the f test using the p value method

Answer 18

F.DIST.RT, multiply this by 2 for a 2 tailed test

Question 19

what is the requirements for the F test

Answer 19

both populations MUST be normally distributed (no CLT here)

Question 20

for paired samples we do a ___ test?

Answer 20

t

Question 21

for a paired t test we use excel to find the difference (which we need to define) and the ___________ to do the calculations

Answer 21

averages, standard deviations

Question 22

what is degrees of freedom for a paired t test

Answer 22

number of differences - 1

Question 23

what are the requirements of the paired t test

Answer 23

• number of differences is large enough for the CLT to apply

- the population of differences is normally distributed

Question 24

for differences in population proportions we do a ___ test

Answer 24

independent samples z test

Question 25

what are the requirements for an independent samples z test for proportions

Answer 25

• random and independent samples
• conditions for binomial satisfied
• normal approximation to the binomial can be used ie. n1*phat 1 greater than or equal to 5 and same with the complement and with the 2’s

Question 26

what are the degrees of freedom for a small samples hypothesis test for the difference in independent population means assuming unequal population variances

Answer 26

smaller of (n1-1) and (n2-1)

Question 27

what are the requirements for the difference in independent population means assuming unequal population variances t test

Answer 27

• random and independent samples
• if a sample is small then the population from which that sample is drawn is normally distributed
• the unknown population variances are not assumed to be equal

Question 28

if there is any doubt about whether the variances are equal, which test should you use?

Answer 28

the unequal variances formulas/test

Question 29

we can run tests through which feature in excel

Answer 29

data analysis

Question 30

what does k represent for a chi squared test

Answer 30

the number of categories or outcomes

Question 31

what are the null and alternative hypotheses for the one way chi squared test (goodness of fit test)

Answer 31

null - the underlying population proportions follow the model

alternative - they do not follow the specified model

Question 32

the chi squared distribution is what shape

Answer 32

right skewed

Question 33

the degrees of freedom for the chi squared goodness of fit test is?

Answer 33

k - 1

Question 34

what are the requirements for the chi squared goodness of fit (one way) test

Answer 34

• The data is from a random sample of independent observations
  
  • For each category the expected count is at least 5

Question 35

what are the null and alternative hypotheses for the chi squared test for independence (two way)

Answer 35

null - the two variables are independent

alternative - the two variables are not independent

Question 36

what is the degrees of freedom for the chi squared independence test

Answer 36

(r - 1) x (c - 1) where r is the number of rows and c is the number of columns

Question 37

the expected value for a cell for the chi squared test for independence is given by?

Answer 37

the row total x the column total/overall total - use this as E in the equation

Question 38

what simple formula can we use in excel to get a P value for a chi squared test

Answer 38

CHISQ.TEST

Question 39

r squared is given by

Answer 39

explained sample variation/total sample variation

Question 40

zero slope means zero?

Answer 40

relationship

Question 41

zero slope means?

Answer 41

measuring the x variable will not help in predicting the y value

Question 42

the null hypothesis testing for the slope parameter beta 1 is?

Answer 42

that b1 = 0 aka the model is not useful for prediction because there is zero slope/relationship

Question 43

the alternative hypothesis testing for the slope parameter beta 1 is?

Answer 43

that b1 is not equal to 0 aka the model is useful for prediction because there is a relationship

Question 44

where do we get values for the tests for regression (test stats, p values, confidence intervals, degrees of freedom etc.)

Answer 44

the regression output

Question 45

what do we use the F test for

Answer 45

to assess the overall model - this is the same as testing if the slope is 0

Question 46

what are the 4 linear regression assumptions for the residuals

Answer 46

• mean of the distribution of the residuals = 0
• distribution of the residuals is normal
• distribution of the residuals has constant variance
• residuals are independent