Fifty students can choose between four different professors to take Introductory Statistics. The number choosing each professor is shown below.

statistics

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Exercise VI

 

Ice Cream Flavor Preference by Gender


 

 

Men

Women

Marginal Row Totals

Vanilla

15

10

25

Chocolate

30

5

35

Marginal Column Totals

45

15

60    (Grand Total)


The chi-square statistic is 5.143. The p-value is .0233. This result is significant at p < .05.


#1. The chart above shows male and female preferences for vanilla vs. chocolate ice cream among men and women.

  1. What percent of men prefer chocolate over vanilla? ________
  2. What percent of women prefer chocolate over vanilla? ________
  3. Report the results of the statistical test in plain language:

#2. The calculator at this link will allow you to perform a one-way chi-square or “goodness of fit test”: 
http://vassarstats.net/csfit.html

Fifty students can choose between four different professors to take Introductory Statistics. The number choosing each professor is shown below. Use the calculator above to test the null hypothesis that there is no preference for professors -- that there is an equal chance of choosing each of them. Report your results including chi-square, degrees of freedom, p-value and your interpretation. Use an alpha level of .05. Be careful not to over interpret – state only what the test result tells you.

Professor

N

Dr. Able

20

Dr. Baker

8

Dr. Chavez

14

Dr. Davis

8

 
#3. Match these non-parametric statistical tests with their parametric counterpart by putting the corresponding letter on the line.
_____ Friedman test
_____ Kruskal-Wallis H test
_____ Mann-Whitney U test
_____ Wilcoxon Signed-Ranks T test
 
A: Paired-sample t-test
B: Independent-sample t-test
C: One-way ANOVA, independent samples
D: One-way ANOVA, repeated measures
 

#4.  Perform a chi-square test to look at the relationship between region of the country (REGION) and financial comfort (FCOMFORT).  Using alpha = .05, what would you conclude from your test: 
 
a.  Financial comfort differs depending on the area one lives in.  
b.  People living in less expensive areas are more likely to report that they are financially comfortable.  
c.  There is not a significant relationship between region and financial comfort. 

d.  People living in the northeast region are most likely to report that they are financially struggling.


#5.  Perform a chi-square test to look at the relationship between college graduation (COLLEGE) and financial comfort (FCOMFORT).  Notice how FCOMFORT is coded, 1=Comfortable, 2=Struggling. Using alpha = .05, what would you conclude from your test?

  1. College graduates are more likely to be financially comfortable than non-graduates
  2. College graduates are less likely to be financially comfortable than non-graduates
  3. There is not a significant difference between college graduates and non-graduates with regard to financial comfort
  4. Graduating college will generally increase your income

#6. Looking at the results of your chi-square test and the associated crosstabs table, what percentage of college graduates report that they are financially comfortable?

  1. 41%
  2. 47%
  3. 53%
  4. 59%

 

#7. What is the phi-coefficient for the relationship between college graduation and financial comfort?

  1. -.470
  2. -.331
  3. -.255
  4. -.118

 

#8. Now look at the relationship between marital status (MSTAT) and college graduation using a chi-square test. What would you conclude?

  1. Married people are more often college graduates than singles
  2. College graduates are more often married than non-graduates
  3. There is not a significant relationship between marital status and college graduation
  4. Both “a” and “b” are true

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