chapter 12

Question 1

When testing 3 or more population proportions, what is the null hypothesis

Answer 1

Ho - all proportions are equal

Question 2

When testing 3 or more population proportions what is the alternative hypothesis

Answer 2

Ha - not all population proportions are equal

Question 3

what does k represent

Answer 3

3 or more population proportions

Question 4

what is the degrees of freedom for testing 3 or more population proportions

Answer 4

k - 1 = df
ie.
3 pops

3 - 1 = 2 degrees of freedom

Question 5

what distribution do we use when testing 3 or more population proportions

Answer 5

chi-squared

Question 6

what does Pi stand for

Answer 6

is the proportion of the population I, 1 <= I <=k

Question 7

if the chi-square test computations indicate Ho can be rejected, we have what

Answer 7

statistical evidence to conclude that not all k population proportions are equal

further analysis can be done to conclude which pop proportion or proportions are significantly different from others

Question 8

What do you need in order to see if 3 or more pop proporitons are equal

Answer 8

1. observed frequencies
2. expected frequencies
3. Chi-squared test statistic for the test of equal pop proportions

Question 9

What does each pop sample provide

Answer 9

categorical data

Question 10

How are the expected frequencies determined with what assumption

Answer 10

that Ho is true

Question 11

What is the chi-squared test statistic used for

Answer 11

to determine whether there is a significant difference between the observed and the expected frequencies

Question 12

How do you calculate the expected frequencies

Answer 12

by using the total column and calculating “likely” total for all populations / the total number of all populations
- then apply this % to each of the populations to determine the expected frequencies

Question 13

What is the degrees of freedom for a chi-square test statistic

Answer 13

k-1

Question 14

what does the expected frequency need to be at least

Answer 14

5 or more for each cell

Question 15

How do you calculate the test stat for tes of equal pop proportions?

Answer 15

1. find the differences between observed and expected frequencies
2. sqaure the difference
3. divided the squared difference by expected frequency
4. add the last column up gives you your chi-square total
5. go to the chi-square distribution chart and with the correct degrees of frequency, find what the p-value will be between then compare to the level of significance

Question 16

where is the chi-square test for equal population proportions will always be (what kind of tail test)

Answer 16

an upper tail test with rejection of Ho occurring when the test statistic is in the upper tail of the chi-square distribution

Question 17

when using the critical value approach, what numbers are you comparing?

Answer 17

the value in the squared difference divided by expected frequency and the where the level of significance is with the correct degrees of freedom on teh chi-square distribution table

Question 18

If p-value is less than the level of significance then what

Answer 18

reject HO

Question 19

if chi-squared value for the squared differences is more than the chi-squared value for the level of significance than what

Answer 19

reject Ho

Question 20

What is the multiple comparison procedure used for

Answer 20

• used when the chi-squared test concludes that the pop proportions of 3 pop are not all equal
• this will help identify the differences in the pop proportions

Question 21

Using the Marascuilo Procedures what are the steps

Answer 21

1. compute the absolute value of the pairwise difference between sample proportions for each pair of pops in the study
2. select a level of significance and compute the corresponding critical value for each pairwise comparison using the formula
3. determine if there are significant differences

Question 22

What is the CV formula for the Marascuilo pairwise comparison procedure

Answer 22

see formula

Question 23

What is the test of independence

Answer 23

using sample data to test for the independence of two categorical variables

Question 24

How does the test of independence work

Answer 24

• we take a sample and record the observations for two categorical variables
• we summarize the data by counting the number of responses for each combination of category for variable 1 and a category for variable 2
• the null hyp for this test is that the two categorical variables are independent

Question 25

What is this an example of Ho: beer preference is independent of gender Ha: beer preference is not independent of gender

Answer 25

Test of independence

Question 26

Goodness of fit test - Definition

Answer 26

A chi-square test - used to test that a population probability distribution has a specific historical or theoretical probability distribution. - This test is for both a multinomial probability distribution and a normal probability distribution.

Question 27

Marascuilo procedure

Answer 27

A multiple comparison procedure that can be used to test for a significant difference between pairs of population proportions. This test can be helpful in identifying differences between pairs of population proportions whenever the hypothesis of equal population proportions has been rejected

Question 28

Multinomial probability distribution

Answer 28

A probability distribution where each outcome be-longs to one of three or more categories. - extends the binomial probability from two to three or more outcomes per trial

Question 29

Test of independence

Answer 29

A chi-square test that can be used to test for the independence between two categorical variables. If the hypothesis of independence is rejected, it can be concluded that the categorical variables are associated or dependent

Question 30

What is the Chi-square test used for

Answer 30

1. test of equality (P1=p2=p3) 2. Test for independence 3. Goodness of fit test (1. is there a change in pop proportion or 2. test if it has a normal prob distribution)

Question 31

When you do a test of equality, If you reject HO and conclude that not all pops are equal, what can you do

Answer 31

1. use Marascuilo procedure to determine where the differences among the proportions exists

Question 32

what are the steps when you are conducting a goodness of fit test to see whether a sample appears to come from a normal probability distribution?

Answer 32

1. order from smallest to largest 2. calculate the mean and standard deviation 3. define intervals n/k (k being the number of sections you want/ intervals) ie 25/5 = 5 4. find the interval limits - use normal table 1/k x 100 = ie 1/5 = 0.2 - 20th percentile 5. look on the z table to find 0.2 x= .84 this is for upper limit and lower is -.84 6. then find the next one - 40th percentile??why 6. Find interval limits z = -.84 M+ SD/-.84 = 56.72 z = .84 M+SD/.84 = 85.82 z = -.25 M + SD/-.25 = 66.75 z = .25 M+SD/.25 = 75.25 8. Find the observed frequencies by putting the total number in each category 9. calculate the test statistic x2 with df - k-p-1 10. calculate the expected frequency - (n/k for all categories)

Question 33

What are some applications of the chi-squared test?

Answer 33

1. Testing equality of population proportions for 3 or more populations 2. Testing the independence of two Categorical variables 3. Testing whether a prob distribution for a population follows a historical or theoretical prob distribution

Question 34

is the Chi-square test restricted to equal sample sizes for each of the k populations?

Answer 34

no

Question 35

Why are we using the chi-squared test for pops are equal

Answer 35

chi-square test statistic to determine whether there is a significant difference between the observed and expected frequencies.

Question 36

if the differences between the observed and expected frequencies are low, then what can we say

Answer 36

If this is the case, the value of the chi-square test statistic will be relatively small and H0 cannot be rejected

Question 37

What type of test is used for testing of equality, proportion and independence

Answer 37

The chi-square test presented in this section is always a one-tailed test with the rejection of H0 occurring in the upper tail of the chi-square distribution

Question 38

Each of the k populations in this section had two response outcomes, Yes or No. In effect, each population had a ______distribution with parameter p the population pro-portion of Yes responses. The degrees of freedom here is _________. An extension of the chi-square procedure in this section applies when each of the k populations has 3 or more possible responses. In this case each population is said to have a __________distribution. the degrees of freedom here is ________________

Answer 38

binomial df= k-1 Multinomial df = (r-1) (k-1) r = # of responses or rows?

Question 39

This chi-square test for test of independence is also a ________ test with rejection of H0 occurring in the _____ tail of a chi-square distribution with _______ degrees of freedom. x2

Answer 39

One tailed test Upper tail (r-1)(c-1) df

Question 40

What is a multinomial distribtuion

Answer 40

it is an extension of the binomial distribution - binomial describes pops whos elements are one of two things success or failure Multinomial distribution describes pops whose elements are one of many things, but a fixed number of things such as years of experience

Question 41

What are the attributes of a multinomial distribution

Answer 41

1. each element of the pop belongs to one, and only one, of k categories 2. The prob that an element form the pop taken at random will be in category i is some unknown but fixed positive number pi, with pi between o and 1 3. a random sample from the pop is taken and each element in the sample is classified into one of k categories

Question 42

The test for goodness of fit is always a _____tailed test with the rejection occurring in the ____tail of the chi-square distribution

Answer 42

one tailed Upper tail

Question 43

Goodness of fit for a normal distribution. Because the normal prob distribution is continuous what must we do

Answer 43

we must modify the way the categories are defined and how the expected frequencies are computed

Question 44

With a continuous probability distribution, establish intervals such that each interval has an expected frequency of ____ or more

Answer 44

5 or more

Question 45

What can be used to determine the boundaries in a normal prob distribution

Answer 45

standard normal probability tables

Question 46

Chi- sqayre test to determine Normal diatribution steps

Answer 46

1. Defibe intervals (each must have a min of 5 per interval) take total and divide by 5 maybe 2. Find interval limits using normal table If intervals are 25/5 = 5 then 1/5 = .2 or 20th percebtike - look on z table for this number (Upper limit) z= 0.25 Then 2/5= .4 find the z number Z= 0.84 3. Limits Z= 0.84. xbar+Sd/-.84=56.72 Xbar+sd /.84 = 85.28 Z=.25 Xbar+sd / -.25 =66.75 Xbar+sd/.25= 75.25 4. Find the oberserved frequencies and our them in their categiries 0-56.72 - has 7 56. 73 - 66.75 has 7 66. 76-75.25 has 1 75. 26 - 85.28 has 1 85. 29 plus has 9 5. Conpute chi square test Expected is 5 all the way theough Df = k-p-1

Question 47

Marascuillo procedures is used for

Answer 47

testing the equality of 3 or more pop proportions

Question 48

In a normal distribution with 30 observations what would the expected number be

Answer 48

30/5 = 6 6 indicates intervals 5 is the expected number for each

Question 49

what is the degrees of freedom for the normal distribution

Answer 49

k-p-1 p = 2 for mean and sd k is the total number of observations

Question 50

Using the Marascuillo procedure, when comparing phat 1 - phat 2 to cv12 what is significant

Answer 50

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