Question 1 You are conducting a test of homogeneity for the claim that two diffe

ID: 3119040 • Letter: Q

Question

Question 1

You are conducting a test of homogeneity for the claim that two different populations have the same proportions of the following two characteristics. Here is the sample data.

The expected observations for this table would be

What is the chi-square test-statistic for this data?
2=

Report all answers accurate to three decimal places.

Question 2

You are conducting a test of independence for the claim that there is an association between the row variable and the column variable.

The expected observations for this table would be

What is the chi-square test-statistic for this data?
2=

Report all answers accurate to three decimal places.

question number 3

You intend to conduct a test of independence for a contingency table with 8 categories in the column variable and 4 categories in the row variable. You collect data from 945 subjects.

What are the degrees of freedom for the 2 distribution for this test?
d.f. =

Category Population
#1 Population
#2 A 31 36 B 42 47

Explanation / Answer

Solution

Back-up Theory

1. For contingency chi-square, the expected frequency for (i, j)th cell = (Oi. x O.j)/n where

Oi. = total frequency of ith row, O.j = total frequency of jth column and n = total frequency.

2. Degrees of freedom for (r row x c column) contingency chi-square = (r - 1)(c - 1)

Now, to answer the questions,

Observed Frequency is in Bold font.

Other figures correspond to Expected

Frequency, underlind

Category

Population
#1

Population
#2

Row Total

[(67x73)/156]

= 31.35

[(67x83)/156]

= 35.65

[(89x73)/156]

= 41.65

[(89x83)/156]

= 47.35

Column Total

156

Note: Row total and column total of expected frequencies must also be equal to the corresponding total of observed frequencies.

Chi-square statistics = Sum{(O - E)2/E}

= {(0.352)/31.32} + {(0.352)/35.65} + {(0.352)/41.65} + {(0.352)/47.35} = 0.1225/0.1051

= 1.1656 ANSWER

Can be done identically.

As per Back-up Theory 2, degrees of freedom = (8 - 1)(4 - 1) = 21 ANSWER