[4.25 points] You want to know if gender affects fear of crime. You have data fr
ID: 3052278 • Letter: #
Question
[4.25 points] You want to know if gender affects fear of crime. You have data from a random sample of 75 people and ask them questions about their gender and fear of crime. Here is your data in the form of a contingency table:
Fear of crime
Gender
Low
Medium
High
Total
male
13
7
3
23
female
12
16
24
52
Total
25
23
27
75
What is the independent variable?
What is the level of measurement for the independent variable?
What is the dependent variable?
What is the level of measurement for the independent variable?
Since we want to know whether there is a relationship between these two variables, which test statistic should we calculate?
Fill in the table with expected frequencies under the null hypothesis assumption that gender and fear of crime are independent:
Fear of crime
Gender
Low
Medium
High
Total
male
23
female
52
Total
25
23
27
75
Perform a hypothesis test to determine whether the two variables are independent. Use an alpha level of .05
What is your df?
What is your critical value?
What is the value of your test statistic?
What is your conclusion (do you reject or fail to reject the null hypothesis)?
Provide an interpretation of your test, including all of the important information.
Fear of crime
Gender
Low
Medium
High
Total
male
13
7
3
23
female
12
16
24
52
Total
25
23
27
75
Explanation / Answer
What is the independent variable?
gender is independent
What is the level of measurement for the independent variable?
male, female
What is the dependent variable?
crime rate is dependent
What is the level of measurement for the independent variable?
Low
Medium
High
Since we want to know whether there is a relationship between these two variables, which test statistic should we calculate?
Chisquare test for independent
Given table data is as below
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calculation formula for E table matrix
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expected frequecies calculated by applying E - table matrix formulae
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calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above
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set up null vs alternative as
null, Ho: gender and fear of crime are independent
alternative, H1: gender and fear of crime are dependent
level of significance, = 0.05
from standard normal table, chi square value at right tailed, ^2 /2 =5.991
since our test is right tailed,reject Ho when ^2 o > 5.991
we use test statistic ^2 o = (Oi-Ei)^2/Ei
from the table , ^2 o = 10.207
critical value
the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 3 - 1 ) = 1 * 2 = 2 is 5.991
we got | ^2| =10.207 & | ^2 | =5.991
make decision
hence value of | ^2 o | > | ^2 | and here we reject Ho
^2 p_value =0.006
ANSWERS
---------------
null, Ho: gender and fear of crime are independent
alternative, H1: gender and fear of crime are dependent
test statistic: 10.207
critical value: 5.991
p-value:0.006
decision: reject Ho
MATRIX col1 col2 col3 TOTALS row 1 13 7 3 23 row 2 12 16 24 52 TOTALS 25 23 27 N = 75Related Questions
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