Study Sheet for Final Exam:

 

            The final exam will be in two parts.  For Part 1, you will be asked to run two X2 analyses.  This section will be worth 50 points.  For Part 2, you will be asked to complete 20 multiple choice questions.  Each question will be worth 2.5 points.  This section will be worth 50 points also.  The final exam will count towards 20% of your final grade in the course.

 

Part 1:

A.  You want to know if, at New Paltz, the frequency of people with blue eyes is significantly different from the frequency of people with brown eyes.  You ask 100 people their eye colors.  You assume an alpha level of p < .05.  Here are your results:

 

                                                            Eye color

                                    Blue                                                      Brown

                                    37                                                         51                                

 

1.  In words, what is the null hypothesis?

2.  Compute X2.

3.  What is X2critical?

4.  What is your decision concerning the null hypothesis?  EXPLAIN.

 

B.  According to the World Almanac, 60% of people in the United States are Christian, 10% are Muslim, 4% are Jewish, and 26% are some other religion (In reality, I made these numbers up).  You are curious to see if the religious denominations of people in New York fit these national proportions.  You randomly survey 200 New York citizens asking each what his or her religious denomination is.  You obtain the following frequencies:

 

Christian                       Muslim                          Jewish                          Other

143                               8                                  30                                 19

 

You assume an alpha level of p < .05.

 

1.  In words, what is the null hypothesis?

2.  Compute X2.

3.  What is X2critical?

4.  What is your decision concerning the null hypothesis?  EXPLAIN.

 

Part 2:

You will need to understand the following concepts:

1.  Measures of central tendency

2.  Standard deviation and variance

3.  Z scores

4.  Correlation:  Different patterns of correlation

5.  Correlation:  Correlation and causation

6.  Bivariate regression:  Its purpose

7.  Bivariate regression:  The difference between the raw score and Z-score prediction models.

8.  Relate the concept of alpha level to a binomial probability distribution

9.  Characteristics of a normal distribution (related to raw and Z scores)

10.  Hypothesis testing:  Conclusions that can and cannot be drawn

11.  One-tailed versus two-tailed tests

12.  When to use a population distribution versus a distribution of means

13.  Characteristics of a distribution of means

14.  Type I and Type II error

15.  Statistical Power (what it is and what influences it)

16.  Alpha and Beta

17.  Cohen's d

18.  t-tests:

A.  Fundamental characteristics of t-tests

B.  How the t distribution differs from a normal distribution

19.  Different kinds of t-tests:

A.  Repeated measures t-test (what it is used for and conclusions that can be drawn from it)

B.  Independent means t-test  (what it is used for and conclusions that can be drawn from it)

20.  Analysis of Variance (ANOVA):

A.  Characteristics of the F distribution

B.  Intepreting the equation for F (What MSB and MSW represent)

C.  What influences an obtained F score

D.  What conclusions can and cannot be made based on an ANOVA

 

Answers to Part 1:

A. 

                                                            Eye color

                                    Blue                                                      Brown

                                    37 (44)                                                  51 (44)                         

 

1.  In words, what is the null hypothesis? The number of people with brown eyes is equal to the number of people with blue eyes.

2.  Compute X2.  In this case, for both blue and brown eyed people, E = N/2 = 88/2 = 44

 

X2 =      (O-E)2

        S  ----------

               E

 

= (37-44)2                      (51-44)2

   -----------          +          ----------- = 1.11 + 1.11 = 2.22

       44                              44    

 

3.  What is X2critical? df = (Nc - 1) = 2-1 = 1;  p < .05; X2critical = 3.84

4.  What is your decision concerning the null hypothesis?  EXPLAIN.

You failed to reject the null hypothesis (as X2 was less than X2critical).  You have not found support for the notion that the frequency of people with blue eyes in your population of interest was significantly different from the frequency of people with brown eyes.

 

B.

 

Christian                       Muslim                          Jewish                          Other

143 (120)                       8 (20)                            30 (8)                            19 (52)

 

1.  In words, what is the null hypothesis?  The proportions of people representing the different religious groups in New York are the same as the proportions of people representing these different relgious groups in the country.

2.  Compute X2.  E (the expected frequency) is different for each religious group.  For each group, E = [N*(% of that group in population)]. 

 

X2 =        (O-E)2

        S  ----------  =

              E

 

   (143-120)2                   (8-20)2                           (30-8)2                           (19-52)2

    -----------         +          -------------           +          ----------- +          -------------          

 

       120                           20                                  8                                  52

 

= 4.41 + 7.2 + 60.5 + 20.94 = 93.05

 

3.  What is X2critical? df = (Nc - 1) = 4-1 = 3;  p < .05; X2critical = 7.82

 

4.  What is your decision concerning the null hypothesis?  EXPLAIN.  Reject the null hypothesis (as X2 was greater than X2critical).  The percentages of people belonging to the different religious denominations in New York are significantly different from the percentages for the country.