AP Statistics
4/27/01
Coley / P. Myers / Wylder
Test #14 (Chapter 14)
Name __________________________________________________________
Part I - Multiple Choice (Questions 1-7) - Circle the answer of your choice.
1.
A bivariate set of data relates the amount of annual salary raise and previous performance rating. The least-squares regression
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equation is y = 1,400 + 2,000x , where y is the estimated raise and x is the performance rating. Which of the following
statements is not correct?
(a)
(b)
(c)
(d)
(e)
For each increase of one point in performance rating, the raise will increase on average by $2,000.
This equation produces predicted raises with an average error of 0.
A rating of 0 will yield a predicted raise of $1,400.
The correlation coefficient of the data is positive.
All of the above are true.
2.
A coefficient of determination is found to be 0.81. Which of the following is true?
(a)
(b)
(c)
(d)
(e)
81% of the variation between the variables is accounted for in the linear relationship.
81% of the data points lie on a line.
The correlation coefficient is approximately 0.9 .
19% of the variation between the variables is accounted for in the linear relationship.
All of these are true.
3.
If the 90% confidence interval for the slope of a regression line does not contain 0, then which of the following is a valid
conclusion?
(a)
(b)
(c)
(d)
(e)
The confidence interval is not valid.
A significance test will not be significant at the 10% level.
There is sufficient evidence to conclude that the slope of the true regression line is 0.
There is sufficient evidence to conclude that the slope of the true regression line is 0.
None of these is valid.
In questions 4-7, use the following printout of the linear regression relating the SAT Math scores of 200 randomly chosen college
freshmen and their first semester GPA’s.
The regression equation is
GPA = 1.53 + 0.00170 Math
Predictor
Constant
Math
Coeff
1.5264
0.0016990
StDev
0.3981
0.0006098
4. The value of SEb for this regression is:
(a)
(b)
(c)
(d)
(e)
.0006098
.0016990
.006
.3981
1.5264
5. The test statistic for a test of significance for a non-zero slope is:
(a)
(b)
(c)
(d)
(e)
.0006098
.3891
2.79
3.83
None of these.
T
3.83
2.79
P
0.000
0.006
6. Which of the following is a valid conclusion that could be drawn from this regression analysis?
(a)
(b)
(c)
(d)
(e)
There is sufficient evidence to reject the hypothesis that   0 .
There is not sufficient evidence to reject the hypothesis that   0
This test is not significant at the 1% level.
Significance cannot be determined from this printout.
None of these is a valid conclusion.
7. Which of the following is the 95% confidence interval for the population slope?
(a)
(b)
(c)
(d)
(e)
(.0005, .0029)
(.0129, .0211)
(-.0170, .0340)
(.0008, .0026)
None of these.
Part II – Free Response (Questions 8-9) – Show your work and explain your results clearly.
8.
A new process designed to increase the temperature inside steel girders shows great promise. In a test of 90 randomly selected
girders, the following regression was performed; a partial computer printout is displayed:
Predictor
Constant
Temp 1
Coeff
0.2074
1.05651
StDev
0.2318
0.02221
S= 0.6009
R-Sq = 96.3 %
R-Sq(adj) = 96.2 %
T
0.89
?
Temp 1 is the initial temperature and Temp 2 is the temperature after the process has terminated.
(a) State the regression equation.
(b) Interpret the slope of the regression in the context of the problem.
(c) Interpret the value of R-Sq in words.
(d) Find the values of T and P indicated by the question marks in the printout.
P
0.373
?
9.
A midterm exam in Applied Mathematics consists of problems in 8 topical areas. One of the teachers believes that the most
important of these, and the best indicator of overall performance, is the section on problem solving. She analyses the scores of 36
randomly chosen students using computer software and produces the following printout relating the total score to the problem
solving subscore, ProbSolv:
Predictor
Constant
ProbSolv
Coeff
12.960
4.0162
StDev
6.228
0.5393
S= 11.09
R-Sq = 62.0 %
R-Sq(adj) = 60.9 %
T
2.08
7.45
P
0.045
0.000
(a) What is the predicted Total Score is the ProbSolve scores was 20 ?
(b) What is the residual for the data point (10, 55) ?
(c) Calculate the 95% confidence interval of the slope of the regression line for all Applied Mathematics students.
(d) Use the information provided to test whether there is a significant relationship between the problem solving subsection and the
total score at the 5% level.
(e) Are the decisions reached through the construction of the confidence interval and through the use of a significance test consistent.
Explain the reasons for your answer.
10. From your textbook on loose leaf paper or reverse side, complete pp. 725- 727 # 63,65,71
Complete pp. 725- 727 # 65
Complete pp. 725- 727 # 71
Complete pp. 725- 727 # 63