Statistics - Hypothesis Testing

Question 1

what type of situations would you apply hypothesis testing

Answer 1

is a population parameter different from a predicted value, difference between two observations on each of the elements of a population (paired measurements), difference between two groups of a population

Question 2

what is a hypothesis

Answer 2

a statement about the value of a population parameter or probability distribution

Question 3

what is H0 and what does it typically indicate

Answer 3

the null hypotheses which typically indicates no difference

Question 4

what is H1 and what does it typically indicate

Answer 4

the alternative hypothesis which typically indicates some difference eg <, >, ≠

Question 5

what is the test idea

Answer 5

take a random sample, test if there is sufficient evidence to reject the null hypothesis in favour of the alternative hypothesis

Question 6

what is a type I error

Answer 6

rejecting H0 when it should have been accepted

Question 7

what is a type II error

Answer 7

accepting H0 when it should have been rejected

Question 8

what is the meaning of the confidence level in hypothesis testing

Answer 8

α is the maximum probability with which we are willing to risk a type I error, ie rejecting H0 when it is correct

Question 9

what are the seven general steps to a hypothesis test

Answer 9

1. decide null hypothesis
2. decide alternative hypothesis
3. decide significance level
4. calculate observed value of test statistic
5. find tabulated test statistic
6. compare values from 4 and 5
7. state conclusion

Question 10

what is μ0

Answer 10

the predicted mean

Question 11

for a one sample t-test what is the calculated test statistic Calc T

Answer 11

(xbar - μ0)/(s/sqrt(n))

Question 12

for a one sample t-test what is the tabulated test statistic Tab T for one sided tests

Answer 12

tn-1;α

Question 13

for a one sample t-test what is the tabulated test statistic for a two sided test

Answer 13

tn-1;α/2

Question 14

for a one sided t-test what is the rejection criteria for H0 if H1 is μ > μ0

Answer 14

Calc T>Tab T

Question 15

for a one sided t-test what is the rejection criteria for H0 if H1 is μ < μ0

Answer 15

Calc T<-Tab T

Question 16

for a two sided t-test what is the rejection criteria for H0 if H1 is μ ≠ μ0

Answer 16

|Calc T|>Tab T

Question 17

what is the p-value of the test

Answer 17

assuming H0 is true, the probability that the calculated test statistic will take on values as extreme or more extreme than the observed test statistic computed from the sample data

Question 18

a small p-value computed from the sample data shows

Answer 18

strong evidence against H0

Question 19

what is the p-value for the one sided t-test H1:μ > μ0

Answer 19

P(T>Calc T)

Question 20

what is the p-value for the one sided t-test H1:μ < μ0

Answer 20

P(T<-CalcT)

Question 21

what is the p-value for the two sided t-test

Answer 21

P(T<-Calc T)+P(T>CalcT)

Question 22

what is the rejection criteria in terms of the p-value

Answer 22

H0 is rejected if p-value>α, where α is the confidence level

Question 23

Paired data (X1,Y1),…,(Xn,Yn) are pairs of random variables satisfying what criteria

Answer 23

Xi and Yi can be related to each other and Xi is independent of all the rest of the variables

Question 23

how do we go about a t-test for paired data

Answer 23

reduce it to a two sided one sample t-test by calculating a new r.v which shows the difference, calculate xbar and s from this set of values

Question 24

what is the null hypothesis for paired data t-test

Answer 24

H0: μd = 0

Question 25

what is the alternative hypothesis for paired data t-test

Answer 25

H1 : μd ≠ 0

Question 26

what is being tested for in a two sample t-test

Answer 26

a difference in the population means

Question 27

what is the null hypothesis for a two sample t-test

Answer 27

H0: μ1 = μ2

Question 28

what is the one sided alternative hypotheses for a two sample t-test

Answer 28

H1: μ1 > μ2

Question 29

what is the two sided alternative hypothesis for a two sample t-test

Answer 29

H1 : μ1 ≠ μ2

Question 30

for a two sample t-test how do you obtain the case μ1< μ2

Answer 30

by exchanging X1 and X2

Question 31

what is the calculated test statistic Calc T for a two sample t-test

Answer 31

(xbar1-xbar2)/(sp*sqrt(1/n1+1/n2))

Question 32

what is sp^2

Answer 32

the pooled variance

Question 33

what is the pooled variance

Answer 33

the weighted average of the two sample variances s1^2 and s2^2

Question 34

for a two sample t-test what does T~tn1+n2-2 mean

Answer 34

the samples of X1 and X2 are normally distributed and the population variances σ1^2 and σ2^2 are equal and they have a t-distribution with v=n1+n2-2 degrees of freedom

Question 35

for a two sample t-test how can we know if σ1^2 and σ2^2 are equal

Answer 35

we can assume this if 1/2<s1^2/s2^2<2

Question 36

what is the tabulated test statistic Tab T for a two sample, one-sided t-test

Answer 36

tn1+n2-2;α

Question 37

what is the tabulated test statistic Tab T for a two sample, two-sided t-test

Answer 37

tn1+n2-2;α/2

Question 38

what are the rejection criteria for H0 for two sample t-tests

Answer 38

the same as 1 sample t-tests if Calc T or |Calc T| are >= Tab T

Question 39

when would we use a z-test

Answer 39

when the degrees of freedom is more than 30

Question 40

what is the only difference between the t-test and the z-test

Answer 40

the tabulated statistic Tab Z

Question 41

what is the tabulated statistic for the z-test

Answer 41

the critical values for the standard normal which is the critical values of the t distribution with infinite degrees of freedom

Question 42

what is Tab Z for one sided z-tests

Answer 42

zα

Question 43

what is Tab Z for two sided z-tests

Answer 43

zα/2

Question 44

does Tab Z change for a two sample z-test

Answer 44

no, Tab Z does not depend on sample size