Statistics / Mr. Hansen
4/21/2004


Check one:

                 Name: __________________________________
c Regular time (36 minutes)
c Extended time (54 minutes)

Test on Chapters 13 and 14, Version 2

Instructions and Scoring.

  • Show all work and answers on separate sheets.
  • Show as much work as time provides. Justify all steps except for algebraic simplification or area calculations. For full credit, you should show the details of s.e. and m.o.e. calculations to the extent possible.
  • You will not earn full credit for a correct answer without adequate justification, or a correct answer without correct notation.

 

 

 

 

1.

An AP Statistics teacher at an eastern prep school is curious if there is an association between eye color and sock-wearing behavior. He has performed a census of the upper three forms and has obtained the following data:

 

 

 

Proper Socks

Improper Socks (not crew style)

Total

 

68
77
21

12
16
10

95
107
35

 

 

 

Note that some students do not wear socks. The first row is for brown- or black-eyed students, the second row is for green- or hazel-eyed students, and the third row is for blue-eyed students or students with a color not listed.

 

 

(a)

Explain why the table shown above is not a 2-way table. Transform it into a 2-way table with 3 rows and 3 columns. Write your table with row and column labels, and raise your hand before continuing.

 

 

(b)

Show your work for the calculation of the expected count for the cell in row 2, column 2.

 

 

(c)

What do the data show regarding the research question? Show all steps, but your work can be extremely abbreviated.

 

2.

Researchers are interested in the relationship between weight and vocabulary size for Lower Schoolers. Specifically, they wish to know whether weight can be used as a predictor of the number of words a student has in his vocabulary. The following data came from an SRS of students:

 

 

 

 


Weight (lbs.)

Estimated Vocabulary
(thousands of words)

 

 

 

75
90
95
100
102
115
125
130
132

9
12
13
14
20
19
38
25
26

 

 

 

 

 

(a)

Describe the relationship between the variables, using words that indicate the context of the problem. Provide at least one diagram and at least one piece of quantitative evidence to support your claim.

 

 

(b)

Using weight as a predictor of vocabulary, state the line of best fit as a mathematical model in which variables are defined.

 

 

(c), (d)

Interpret both the slope and the y-intercept in part (b) in the context of the problem, using words such as “weight” and “vocabulary.” Your answers should make sense to someone who has studied little or no statistics.

 

 

(e)

Compute the standard error of the slope (what the AP would call “standard deviation of the slope”) for the linear regression model. Show brief work only.

 

 

(f)

Perform a significance test for the proposition that the true correlation coefficient is positive. Show all steps.

 

 

(g)

BONUS: What lurking variable would probably serve as a better predictor of vocabulary size?