A survey of a random sample of 100 adults was taken and their personality type (

Question

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. 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 researcher Goodness of Fit Test of Homogeneity Test of Independence 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 0 2 22 22.2 23 25 37 60 The data were entered into R and part of the output is provided If there is no relationship between personality type and their attitude toward small cars for the population of all such adults. what is the expected value of the test statistic 0 0.495 1.405 2 Does there appear to be a statistically significant relationship between personality type and their attitude toward small cars for the population of all such adults Use a 5% significance level, select your answer, and think about the reasoning behind your answer. Yes No

Explanation / Answer

5.a.

When we have a contingency table like this, it is

OPTION C: Test of independence [ANSWER]

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5.b

Note that

E(x) = (Row Total)(Column Total)/(Grand Total) = 60*37/100 = 22.2 [ANSWER]
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5.c.

If there is no relationship, the expected and observed values would nearly be equal, so the chi squares statistic will be

OPTION A: 0 [ANSWER]

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5.d.

As P = 0.495 is large, then there is no significant relationship, so

OPTION B: NO [ANSWER]

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