Question 6 Background Personality and Attitude A survey of a random sample of 10

Question

Question 6 Background Personality and Attitude A survey of a random sample of 100 adults was taken and their personality type (A or B and their attitude toward small cars (positive, neutral, negative) were recorded. The data are summarized in the table shown. Attitude Toward Small Cars Personality Type Positive Neutral Negative Total Type A 25 111 24 60 Type B 12 40 Total 37 20 43 100 Question 6 Subquestions 6.a The researcher is interested in assessing if there is a relationship between personality type and their attitude toward small cars for the population of all such adults. What is the name of the statistical test being performed by the point(s) researcher? Goodness of Fit Test of Homogeneity Test of Independence 6.b If there is no relationship between personality type and their attitude toward small cars for the population of all such adults, how many Type A adults would you have expected to have a positive attitude toward small cars? point(s) 22 22.2 23 25 37 60

Explanation / Answer

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: no relation b/w X and Y OR X and Y are independent
alternative, H1: exists a relation b/w X and Y OR X and Y 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 = 1.405
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| =1.405 & | ^2 | =5.991
make decision
hence value of | ^2 o | < | ^2 | and here we do not reject Ho
^2 p_value =0.495

ANSWERS
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null, Ho: no relation b/w X and Y OR X and Y are independent
alternative, H1: exists a relation b/w X and Y OR X and Y are dependent
test statistic: 1.405
critical value: 5.991
p-value:0.495
decision: do not reject Ho                              

6.a.
goodness of fit

6.b.1
type A adults expected to have a positive attitude is 22.2

6.c.1
test statistic, 1.405

col1 col2 col3 row 1 25 11 24 60 row 2 12 9 19 40 TOTALS 37 20 43 N = 100

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