The table below shows the frequencies for the favorite color of both introverts
ID: 3294248 • Letter: T
Question
The table below shows the frequencies for the favorite color of both introverts and extraverts. Test the hypothesis that personality type is independent of color preference. Use = .05. Be sure to state your hypotheses, find your critical value, calculate your test-statistic, and evaluate the null hypothesis. Also state a conclusion. Introvert : Blue 8. Red 3, Yellow 1. Extravert :Blue 2, Red 8, Yellow 2.
STEP 1: State your hypotheses. STEP 2: Set up the criteria for making a decision. STEP 3: Summarize the data into the appropriate test-statistic. STEP 4: Evaluate H0. (Reject or Fail to reject)
Conclusion:
Use SPSS to help you answer the questions above. Turn in both your answers to these questions as well as your SPSS output file.
Note that you must enter the raw data in order for SPSS to perform the correct computation. You cannot enter the numbers as they are printed above! Use that summary information only if you wish to check your work by hand. When using SPSS we must enter one participant’s data on each line. The data you will use with SPSS are printed below:
Subject # Personality Color Preference
1 Introverted Blue
2 Introverted Blue
3 Extraverted Red
4 Extraverted Red
5 Extraverted Yellow
6 Introverted Red
7 Introverted Blue
8 Extraverted Blue
9 Extraverted Red
10 Introverted Yellow
11 Introverted Blue
12 Introverted Blue
13 Extraverted Red
14 Extraverted Red
15 Extraverted Blue
16 Introverted Red
17 Introverted Blue
18 Extraverted Red
19 Extraverted Red
20 Introverted Blue
21 Extraverted Yellow
22 Extraverted Red
23 Introverted Red
24 Introverted Blue
25 Extraverted Red
You will enter that participants personality (1=introverted, 2= extraverted) in the first column (VAR1), and you will enter that participants color preference (1=blue, 2=red, 3= yellow) in the second column (VAR2). So, you should end up with 25 lines as you go down the page, and each line will contain two numbers (VAR1 and VAR).
Once you get the data in, choose Analyze from the menu, then select Descriptive Statistics, and then Cross-tabs. At this point hit the Statistics button on the dialog box. Be sure to check the box next to Chi-Square and hit Continue. Use the arrow buttons in the middle to move your variables over to be tested. VAR1 is your row, and VAR2 is your column. Then hit okay. You can compute the chi-square by hand to check your work.
Explanation / Answer
Answer:
STEP 1: State your hypotheses.
Ho: personality type is independent of color preference.
H1: personality type is not independent of color preference
STEP 2: Set up the criteria for making a decision.
Degrees of freedom for chi square with 22 df = 5.991
Reject Ho if chi square test statistic > 5.991
STEP 3: Summarize the data into the appropriate test-statistic. STEP 4: Evaluate H0. (Reject or Fail to reject)
Calculated chi square =6.904 which is > 5.991 at 0.05 level.
Reject Ho.
Conclusion:
We conclude that personality type is not independent of color preference.
var1 * var2 Crosstabulation
Count
var2
Total
Blue
Red
Yellow
var1
Extraverted
2
9
2
13
Introverted
8
3
1
12
Total
10
12
3
25
Chi-Square Tests
Value
df
Asymptotic Significance (2-sided)
Pearson Chi-Square
6.904a
2
.032
Likelihood Ratio
7.294
2
.026
N of Valid Cases
25
a. 3 cells (50.0%) have expected count less than 5. The minimum expected count is 1.44.
var1 * var2 Crosstabulation
Count
var2
Total
Blue
Red
Yellow
var1
Extraverted
2
9
2
13
Introverted
8
3
1
12
Total
10
12
3
25
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