Lecture 14 and 15

Question 1

hypotheses tests?

Answer 1

hypothesis tests are tests about a population parameter

Question 2

null hypothesis?

Answer 2

is a statement involving equality about a population parameter. We assume the null hypothesis is true to do our analysis

Question 3

Alternative hypothesis?

Answer 3

statement that contradicts the null. What we conclude is true if the experimental results lead us to conclude that our null is false. Does not involve equality

Question 4

If p value < a

Answer 4

reject the null

Question 5

if p-value > a

Answer 5

fail to reject null

Question 6

type I error

Answer 6

deciding to reject null when true, incorrectly supporting alternative

Question 7

type II error

Answer 7

failing to reject the null when false, incorrectly not supporting alternative

Question 8

alpha (probability)

Answer 8

P(type I error)
P(decide to reject null when true)
P(incorrectly supporting the alternative)
significance level of test

Question 9

beta (probability)

Answer 9

P(type II error)
P(failing to reject the null when null is false)
P(incorrectlly not supporting the alternative)

Question 10

1-beta

Answer 10

P(decide to reject null when null is false)
P(correctly supporting alternative)
power of test

Question 11

5 steps to solve hypothesis test

Answer 11

1: formulate null and alternative
2: find test statistic
3: specify level of a
4: calculate test statistic and p value
5: draw a conclusion. state whether or not to reject the null and provide interpretation

Question 12

Different cases

Answer 12

case 1: H0: mu= mu0 vs Ha: mu<mu0 (reject null if z<za)
case 2: H0: mu=mumu0 vs Ha: mu>mu0 (reject null if z>za)
case 3: H0: mu=mu0 vs Ha: mu (not =) mu0 (reject null if z>za/2 or z<-za/2)

Question 13

test statistics for large and small samples

Answer 13

z= sample-population mean/ sd/ sqrt (n)
t= sample-population mean/sample sd/sqrt (n)

Question 14

p-value

Answer 14

(normcdf or tcdf)
P(z>x)
for a specific state test is the probability of observing a vlaue of the test stat that is at least as contradictory to the null hypothesis and supportive of alt hypothesis, as actual one computed from sample data

Question 15

How to determine to reject null

Answer 15

choose maximum value of x of a you are willing to tolerate
if p-value is less than a, reject if not do not reject

Question 16

ethics

Answer 16

selecting value of alpha must be done BEFORE to computing observed sig level (p value)

Question 17

conditions for a valid small sample hypothesis test for mean

Answer 17

random sample is selected form target population
population from which the sample is selected has a distribution that is approximately normal

Question 18

interpretation

Answer 18

at a= ___ level of significance, there is insufficient ( or sufficient) evidence that mean mean is ___ than ___. This means that the data does (or not) supply evidence.

Question 19

Large sample about population proportion

Answer 19

case 1: Ho: p=p0 vs Ha: p<p0 (reject H0 if z<-za)
case 2: H0: p=p0 vs Ha: p>p0 (reject H0 if z>za)
case 3: H0: p=p0 vs Ha: p (not=) p0 (reject H0 if z>za/2)

Question 20

test stat for proportion

Answer 20

z= p(hat)-p/sqrt (pq/n)

Question 21

conditions for large sample test for p

Answer 21

1: a random sample is selected form a binomial population
2: the sample size n is large. this condition will be satisfied if both np0>15 + nq0>15

Question 22

rejection region and p value on calc

Answer 22

invNorm or invT; normcdf or tcdf