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Exam 15: Chi-Square

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Question 1

Multiple Choice

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What does a positive residual in a crosstab cell mean?

A) The two variables are negatively associated.
B) There were more cases with that combination of traits than expected.
C) There were fewer cases with that combination of traits than expected.
D) You should not reject the null hypothesis.

E) A) and C)
F) B) and C)

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B

Question 2

Multiple Choice

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Your research hypothesis is "In the population, there is a relationship between the driver's sex and the type of vehicle being driven." What type of hypothesis test should be used?

A) paired-samples t test
B) independent samples t test
C) one-way ANOVA
D) two-way ANOVA
E) chi-square

F) B) and E)
G) All of the above

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Question 3

Multiple Choice

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If religious affiliation and political party affiliation are independent, then

Fill in the expected frequencies for each of the cells in the following table. $\begin{array} { | l | c | c |c } \hline { } & { \text { ABLEGAL } } \\\hline \text { SEX } & \text { yes } & \text { no } \\\hline \text { male } & &&30 \\\hline \text { female } & & &70\\\hline &70&30&100\end{array}$

Here is a bivariate table with observed counts and expected counts. What is the value of chi-square for this table? $\begin{array} { | l l | c | c | } \hline& & { \text { RACE } } \\\hline \text { SEX } && \text { white } & \text { black } \\\hline \text { male } & \text { observed } &2&6&8\\& \text { expected } & 4 & 4 \\\hline\end{array}$ $\begin{array} { | l r | l | l | l } \hline \text { female }&\text { observed } & 6 & 2&8 \\&\text { expected } & 4 & 4 & \\\hline&&8&8&16\\\end{array}$ chi-square = __________

What does a positive cell residual tell you? A negative cell residual? A zero cell residual?

A cell in a crosstab has an observed count of 50 and an expected count of 25. What is the value of the residual?

Your research hypothesis is "In the population, the average SAT score of persons the second time they take the test is higher than the average of those same persons the first time they took the test." What type of hypothesis test should be used?

A statistical guideline that is widely accepted is not to use chi-square if even one cell has an expected count of _____ or if more than _____ of the cells have expected counts of less than 5.

What kinds of questions can you answer using a chi-square hypothesis test?

You are doing a chi-square test and the sample results are consistent with the research hypothesis. On the basis of the following output, what should you do? Chi-Square Tests $\begin{array}{|l|r|r|r|}\hline & \text { Value } & \text { df } & \begin{array}{c}\text { Asymp. Sig. } \\\text { (2-sided) }\end{array} \\\hline \text { Pearson Chi-Square } & 13.951^{*} & 6 & .030 \\\text { Likelihood Ratio } & 14.910 & 6 & 021 \\\text { Linear-byLinear } & 7474 & 1 & 006 \\\text { Association } & & & \\\text { N of Valid Cases } & 144 & & \\\hline\end{array}$ a. 5 cells $( 41.7 \% )$ have expected count less than 5 . The minimum expected count is 48 .

You gathered your data using a snowball sample which is a non-probability sampling technique. Which of the following inferential procedures may you use to analyze the data?

Chi-square is _____ measure of association.

You want to know if there is a significant relationship between race and academic major. Which would be an appropriate procedure to use?

What is the lowest level of measurement that can be used for the two variables in a chi-square analysis?

Your research hypothesis is that region and race are related. Based on the following table of residuals, the sample results are consistent with the _____ and you should proceed to _____. RACE* REGION Crosstabulation Residual $\begin{array}{|rr|r|r|r|r|}\hline&&\text { REGION }\\\hline && \text { 1 Northeast } & \text { 2 Midwest } & \text { 3 South } & \text { 4 West } \\\hline \text { RACE } & \text { 1 white } & 6.3 & 26.0 & -32.7 & 4 \\& 2 \text { black } & 4.2 & -23.0 & 45.1 & -26.3 \\& 3 \text { other } & -10.5 & -3.0 & -12.4 & 25.9 \\\hline\end{array}$

You are doing a chi-square test and the sample results are consistent with the research hypothesis. On the basis of the following output, what should you do? Chi-Square Tests $\begin{array}{|l|r|r|r|}\hline &{\text { Value }} & \text { df } & {\begin{array}{c}\text { Asymp. Sig. } \\\text { (2-sided) }\end{array}} \\\hline \text { Pearson Chi-Square } & 13.266^{a} & 6 & 039 \\\text { Likelihood Ratio } & 13.442 & 6 & 037 \\\text { Linear-by-Linear } & 1.015 & 1 & .314 \\\text { Association } & & & \\\text { N of Valid Cases } & 342& & \\\hline\end{array}$ a. 1 cells $( 8.3 \% )$ have expected count less than 5 . The minimum expected count is $4.57$ .

You are doing a chi-square problem. Your row variable has two categories. Your column variable has seven categories. How many degrees of freedom will your chi-square have? __________ degrees of freedom

What does it mean if two variables are independent? If two variables are related?

Your research hypothesis is "In the population, males drive at a faster speed on the interstate than females." What type of hypothesis test should be used?