Question 1

Answer the questions that follow this SPSS output: 
PELNTEN ' SEX Crosstabulation
$\begin{array}{|lll|r|r|r|}
\hline &&&\text { 0 male } & \text { 1 female }& \text { total}\
\hline \text { RELINTEN } & \text { 0 no religon }& \text { Count } & 41 & 25 & 66 \
&& \text { Residual } & 8.6 & -8.6 & \
\hline & \text { 1 not very strong } & \text { Count } & 61 & 58 & 119 \
&& \text { Residual } & 2.5 & -2.5 & \
\hline & 2 \text { somewhat strong } & \text { Count } & 16 & 18 & 34 \
&& \text { Residuat } & -7 & 7 & \
\hline  &\text { 3 strong }& \text { Count } & 50 & 73 & 123 \
&& \text { Residuai } & -10.4 & 10.4 & \
\hline \text { Total } && \text { Count } & 168 & 174 & 342 \
\hline
\end{array}$
Chi-Square Tests
$\begin{array}{|l|r|r|r|}
\hline & {\text { Value }} & \text { dr } & {\begin{array}{c}
\text { Asymp. Sig. } \
\text { (2-sided) }
\end{array}} \
\hline \text { Pearson Chr-8quare } & 8.270^{2} & 3 & 041 \
\text { Likelihood Ratio } & 8.332 & 3 & 040 \
\text { Linear-by-Linear } & 7.902 & 1 & 005 \
\text { Association } & & & \
\text { NofValid Cases } & 342 & & \
\hline
\end{array}$
a. 0 cells $ (0 \%) $ have expected count less than 5 . The minimum expected count is 16.70
Your research hypothesis is "In the population, SEX and strength of religious affiliation (RELINTEN) are related." 
A) What is your null hypothesis?
B) Are your sample results consistent with the null hypothesis or the research hypothesis? (null / research)
C) What is the probability of getting the sample results you got if the null hypothesis is true? (If this step in hypothesis testing can be skipped, write the word "SKIP".)
D) What is your conclusion? (In other words, do you "reject" or "not reject" the null hypothesis based on these results?)
E) Are your results statistically significant? (yes / no)

Accepted Answer

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Question 2

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

Accepted Answer

The Chi-Square Test is used to determine whether there is a significant association between two categorical variables. In this case, we want to determine if there is a significant relationship between race (a categorical variable) and academic major (another categorical variable). Therefore, the appropriate procedure to use would be the Chi-Square Test.

Question 3

Your research hypothesis is "In the population, there is a difference in the average speed of persons driving sports cars, minivans, motorcycles, and sedans." What type of hypothesis test should be used?

Accepted Answer

The research hypothesis involves comparing the means of four different groups (sports car, minivan, motorcycle, sedan) which makes a one-way ANOVA the most appropriate test to determine if there is a statistically significant difference in average speed between these groups.

Question 4

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.

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The answer of A statistical guideline that is widely accepted...

Question 5

Your research hypothesis is "In the population, persons drive at an average speed that is greater than 70 mph." What type of hypothesis test should be used?

Accepted Answer

A one-sample t test is appropriate for testing a hypothesis about the population mean when only one sample is available. In this case, the hypothesis is about the population mean driving speed being greater than 70 mph, and we would compare the sample mean to 70 mph using a t test.

Question 6

Variables included in a chi-square hypothesis test can have which levels of measurement?

Accepted Answer

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Question 7

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

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Question 8

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?

Accepted Answer

A paired-samples t test should be used since we are comparing the scores of the same individuals at two different times.

Question 9

What should you do next if chi-square is significant?

Accepted Answer

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Question 10

Answer the question that follows this SPSS output: 
SATJOB * SEX Crosstabulation
$\begin{array}{|lll|r|r|r|}
\hline &&& \text { sex }\
\hline &&&\text { 0 male } & \text { 1 female }& \text { total}\
\hline \text { SATJOB }& 1 \text { very dissatisfed } & \text { Count } & 2 & 4 & 6 \
&& \text { Expected Count } & 2.8 & 3.2 & 6.0 \
\hline &2 \text { a limite dissatisfied } & \text { Count } & 15 & 14 & 29 \
&& \text { Expected Count } & 13.7 & 15.3 & 29.0 \
\hline& {3 \text { moderately satisfled }} & \text { Count } & 62 & 57 & 119 \
&& \text { Expected Count } & 56.4 & 62.6 & 119.0 \
\hline &4 \text { very satisfied } & \text { Count } & 66 & 86 & 152 \
&& \text { Expected Count } & 72.0 & 80.0 & 152.0 \
\hline \text { Total } && \text { Count } & 145 & 161 & 306 \
&& \text { Expected Count } & 145.0 & 161.0 & 306.0 \\hline
\end{array}$
Chi-Square Tests 
$\begin{array}{|l|r|r|r|}
\hline &{\text { Value }} & \text { df } & \begin{array}{r}
\text { Asymp. Sig. } \
(2-\text { sided) }
\end{array} \
\hline \text { Pearson Chi-Square } & 2.714ᵃ & 3 & 438 \
\text { Likelihood Ratio } & 2.726 & 3 & 436 \
\text { Linear-by-Linear } & 761 & 1 & 383 \
\text { Association } & & & \
\text { Nor oalid Cases } & 306 & & \
\hline
\end{array}$
a. 2 cells $ (25.0 \%) $ have expected count less than 5 . The minimum expected count is 2.84
You want to do a chi-square test but the crosstab has an expected count problem. How could you transform one or both of the variables to remedy the problem?

Accepted Answer

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Question 11

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 = __________

Accepted Answer

The answer of Here is a bivariate table with observed...

Question 12

Fill in the expected frequencies for each of the cells in the following table.

$$\begin{array} { | l | c | c |c } 
\hline { } & { \text { ABLEGAL } } \
\hline \text { SEX } & \text { yes } & \text { no } \
\hline \text { male } & &&30 \
\hline \text { female } & & &70\
\hline &70&30&100
\end{array}$$

Accepted Answer

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Question 13

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

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Question 14

What expected counts would indicate that the value of chi-square may be unstable because the cases are too thinly spread across the crosstab?

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Question 15

Answer the questions that follow this SPSS output: 
RELINTEN ' COL.ATH Crosstabulation
$\begin{array}{|lll|r|r|r|}
\hline \text { RELINTEN } & \text { 0 no religon } & \text { Count } & 5 & 41 & 46 \
&& \text { Residual } & -3.8 & 3.8 & \
\hline & \text { 1 not very strong } & \text { Count } & 19 & 72 & 91 \
&& \text { Residual } & 1.6 & -1.6 & \
\hline &{2 \text { somewhat strong }} & \text { Count } & 5 & 18 & 24 \
&& \text { Residual } & 1.4 & -1.4 & \
\hline &{3 \text { strong }} & \text { Count } & 19 & 76 & 95 \
&& \text { Residual } & .8 & -8 & \
\hline \text { Total } && \text { Count } & 49 & 207 & 256 \
\hline
\end{array}$
Chi-Square Tests
$\begin{array}{|l|r|r|r|}
\hline &{\text { Value }} & \text { df } & {\begin{array}{c}
\text { Asymp. Sig } \
\text { (2-sided) }
\end{array}} \
\hline \text { Pearson Chi-Square } & 2.789^{3} & 3 & 425 \
\text { Likelihood Raso } & 3.043 & 3 & 385 \
\text { Linear-by-Linear } & 887 & 1 & 346 \
\text { Association } & & & \
\text { N of Valid Cases } & 256 & & \
\hline
\end{array}$
a. 1 cells (12.5\%) have expected count less than 5 . The minimum expected count is $4.59$.
Your research hypothesis is "In the population, whether or not a person would allow an atheist to teach college (COLATH) and strength of religious affiliation (RELINTEN) are related." 
A) What is your null hypothesis?
B) Are your sample results consistent with the null hypothesis or the research hypothesis? (null / research)
C) What is the probability of getting the sample results you got if the null hypothesis is true? (If this step in hypothesis testing can be skipped, write the word "SKIP".)
D) What is your conclusion? (In other words, do you "reject" or "not reject" the null hypothesis based on these results?)
E) Are your results statistically significant? (yes / no)

Accepted Answer

The answer of Answer the questions that follow this SPSS...

Question 16

For each of the following, calculate the cell residual:
$$\begin{array}{l}
\begin{array} { llll } 
&\text {observed count }&\text { expected count}&\text { residual }\
\hline a.&50&75\
b.&20&20\
c.&90&30\
\end{array}
\end{array}$$

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Question 17

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

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Question 18

What can you do if the expected cell frequencies are too small for a chi-square hypothesis test?

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Question 19

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

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Quiz 15: Chi-Square