QMETH201 FINAL EXAM REVIEW QUESTIONS
Question 1: Probability
Text Chapter 6 Problem 32 on page 231
Question 2: Sampling Distribution - 1
Text Chapter 7 Problem 34 on page 280
Question 3: Sampling Distribution - 2
Text Chapter 8 Problem 24 on page 322
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Question 4: Regression - 1
A prompt reply to a user’s call for support is a critical factor for marketing
software. In a study at a major software firm, the average customer holding time
in minutes for a day (variable Y) and the daily number of calls for support in
1000 (variable X) are collected for 30 randomly selected working days. Below is a
summary of data.
Scatterplot
Summary Table
The average holding time on Y axis.
The number of calls per day on X axis.
Number of Calls
Average
2.394
Std. Dev.
0.315
Correlation Coefficient =
Scatterplot
Average Holding Time in
Minutes
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Holding Time
4.436
0.310
0.0667
4.5
4
3.5
1.5 1.7 1.9 2.1
2.3 2.5 2.7 2.9 3.1
Number of Calls per Day in 1000
A. The regression line superimposed on the scatterplot is determined by means of a
well known criterion in statistics. Please state the name of the criterion and
explain how it works. Please be brief.
(1) The criterion is called:
(2) Explain how it works:
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B. Using the summary table, determine the equation of the regression line. Please
show your work.
(1) The slope of the regression line:
(2) The intercept of the regression line:
C. How much in percentage of the variation of the average customer holding time is
explained by the number of calls? Please show your work.
D. According to your regression equation computed in B, what is the prediction of
the average customer holding time for a day with 2500 calls?
E. Can you compute the standard error of estimate for the prediction computed in
D?
Yes
No
Circle one.
If you circle Yes, compute. Please show your work.
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Question 5: Regression - 2
You are an operation manager of a regional distribution center of United Express.
You want to find out how the number of packages handled in a day in the center is
related to the number of employees sorting them. The relationship will be used for
hiring temporary workers in busy seasons. A random sample of 12 working days are
used to estimate the relationship. Define:
Y = Number of packages handled in the center for day t.
X = Number of workers in the center for day t.
The population regression model used is:
Yt = α + β Xt + ε t
t = 1,2,…12
and ε t follows independently normal (0, σε). Below is the Excel regression output
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.6948
R Square
0.4827
Adjusted R Square
0.4309
Standard Error
44.3916
Observations
12
Intercept
Workers
Coefficients Standard Error
301.1525
79.4521
30.5763
10.0100
A. To check how well your regression model predicts, you select a particular day
from the sample of 12 days. The record for the day shows that the number
handles is 600 units with 9 assigned workers. Answer the following questions.
Please show your work.
(1) The predicted value for the day
(2) The residual
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B. Since you have used a sample of only 12 randomly selected days, you would like
to know how accurately the slope of the regression is estimated. Construct a
95% confidence interval for the slope. Please show your work.
C. Continuation of B You also want to make sure that the regression is not
“illusory.” Please explain what is meant by an illusory regression.
D. Continuation of C. You want to apply a statistical test to confirm that the
regression is not illusory. Please answer each of the following steps:
(1) Write the null and two sided research hypotheses.
(2) You want to apply the t-stat approach at a significance level of 5%.
(3) What kind of error might you have committed?
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