# STUDY GUIDE #2 – STATS

Study Guide for exam 2

This guide starts with the example that we left with in Study guide 1 – as follows:

Here’s an example to work with for many of the computational problems:

Here’s the story:  Your dog, Momo, barks way too much and you can’t figure out why.  One day, you forget to give Momo doggie biscuits and you notice that she does not bark that day.  After thinking about this issue for a bit, you decide to run a study using 3 other dogs to determine whether # of doggie biscuits consumed is indeed related to the amount of barking.  In this study you measure (X) the number of doggie biscuits each dog eats in a day and (Y) the number of times that dog barks, in order to see what the actual relationship is between these two variables.

X (# of doggie biscuits consumed)       Y (# of barks in a day)

0                                                                                  2

1                                                                                  1

2                                                                                  3

1.  Write the Z-score prediction model to predict Zy from Zx.

2.  What is the predicted Zy if Zx = 0?

3. Write the raw-score prediction model to predict Y from X.

4.  Draw scatterplot of raw data showing the correlation between X and Y.

5.  The scatterplot shows that the relationship between X and Y is

A.  very strong and positive.

B.  very strong and negative.

C.  moderate and positive.

D.  moderate and negative.

6.  Draw the regression line on the scatterplot up above.

7.  Compute the proportionate reduction of error (NOT by just squaring “r”).

8.  Based on the proportionate reduction of error, what would you conclude about how well X predicts Y?  EXPLAIN.

9.  Be able to interpret a probability distribution (e.g., the X axis corresponds to values of the variable;
Y axis corresponds to how likely each value is).

10.  Calculate the percentage of cases above and/or below a particular  Z score in a normal distribution.

11.  Calculate the percentage of cases above and/or below a particular  raw score in a normal distribution.

12.  Calculate a particular Z score in a normal distribution given the percentage of cases above and/or below it.

13.  Calculate a particular raw score in a normal distribution given the percentage of cases above and/or below it.

Note that for the content related to hypothesis testing, the following guidance is provided:

1.  Translate a hypothesis into H0, H1, μ1, and μ2.

2.  Completely understand the difference between a one and two tailed test.

3.  Complete all steps in the hypothesis testing if N = 1.

A. Translate the hypothesis into H0, H1, μ1, and μ2.

B.  Determine the comparison distribution.

C.  Determine Zcritical based on the alpha level and number of tails.

D.  Calculate a Z score.

E.  Explain your conclusion.

4.  Complete all steps in the hypothesis testing if N > 1.

A. Translate the hypothesis into H0, H1, μ1, and μ2.

B.  Determine the comparison distribution.

a.  Calculate μm and sigmam.

b.  understand the relationship between the magnitude of N and the variance of a distribution of means.

C.  Determine Zcritical based on the alpha level and number of tails.

D.  Calculate a Z score.

E.  Explain your conclusion.

ANSWER KEY regarding computational questions:

X          –           M         (X-M)                 (X-M)2           Zx

0          –           1          -1                     1                      -1.22

1          –           1          0                      0                      0

2          –           1          1                      1                      1.22

___________________________________

Mx = 1                          SSx = 2

SDx2 = .67

SDx = .82

Y          –           M         (Y-M)                (Y-M)    2           Zy

2          –           2          0                      0                      0

1          –           2          -1                     1                      -1.22

3          –           2          1                      1                      1.22

___________________________________

My = 2                          SSy = 2

SDy2 = .67

SDy = .82

ZxZy

-1.22*0  =          0

0*-1.22  =          0

1.22*1.22=        1.49

___________________

S(ZxZy) = 1.49

r = 1.45/3 = .50

Z score model —->                  Zy(hat) = (.50)(Zx)

Raw score model —->

b = .50(.82/.82) = .50

a = 2 – (1)(.50) = 1.50

—-> Y` = 1.50 + .50(X)

Zy (predicted) if Zx = 0 … Zy = 0

r2 = (SSt – SSe)/SSt …

Error                 Error2

Y                      Y`                      (Y- Y`)               (Y- Y`)2

2                      1.50                  .50                    .25

1                      2                      -1                     1

3                      2.50                  .50                    .25

____________________________________________

SSe = S(Y- Y`)2 = 1.5

— SSt = SSy = 2

r2 = (SSt – SSe)/SSt = (2-1.5)/2 = .5/2 = 1/2*1/2 = .25

(r2 = .50*.50 = .25)