STAT302: 508-510 Final Exam, Form A Fall 1997
1. In reference to simple linear regression, how do
we test the assumption that the variance about
the true regression line is constant?
A. Bartlett’s test for equal variances which is
provided in the output
B. a normal quantile plot of the residuals
C. a residual plot (scatterplot of the residuals)
D. an ANOVA test for equal means
E. the t-test in the regression output
2. Santa wants to know the proportion of kids that
have been naughty this year. If the true propor-
tion is π=0.25 (only he doesn’t know that, but
Mrs. Claus does) and he takes a sample of 100,
what is the distribution of the sample propor-
tion, p?
A. Although the mean would be 0.25, we can’t
determine the distribution.
B. p∼N(0.25,102)
C. p∼N(100,0.252)
D. p∼N(0.25,0.0432)
E. Only Mrs. Claus knows for sure.
3. “Christmas is a coming and the goose is getting
fat”. If X∼N(µ= 15lbs,σ
2=2
2
) is the dis-
tribution of the weight of a goose, which of the
following is/are true?
A. The zscore of the sample median of any
sample of ngeese is 0.
B. The probability that a goose weighs less
than 15 is 0.5.
C. The sample mean of any sample of ngeese
is 15.
D. All of the above are true statements.
E. Exactly two of the two (excluding D.) are
true.
4. Why do we do Two-Way ANOVA rather than
One-Way ANOVA twice?
A. You can save ’money’ by using the same
data, whereas two One-Way ANOVA’s
would need two sets of data.
B. You can test more than one factor, i.e.,two
factors, simultaneously.
C. You can test the interaction between two
factors.
D. all of the above
E. none of the above
5. Which of the following statements concerning
the definition of confidence intervals is true?
A. If I compute 90% confidence intervals for a
population mean from 10 different experi-
ments, then one of the 10 confidence inter-
vals will not contain the true mean.
B. If I compute a 90% confidence interval for
a population mean, then the probability of
this interval containing the true mean is
90%.
C. If I compute a 90% confidence interval for
the mean age of American citizens, then
90% of all Americans’ ages will fall in this
interval.
D. all of the above
E. none of the above
6. You are given a 90, 95 and 99% confidence in-
terval (not necessarily in that order) for the true
population proportion of kids wanting computer
games this Christmas: (0.471, 0.541), (0.460,
0.552), (0.477, 0.535). Which of the following
is the best statement of the p-value for testing
H0:π=0.45 vs. HA:π6=0.45?
A. p-value >0.10
B. 0.10 >p-value >0.05
C. 0.05 >p-value >0.01
D. 0.01 >p-value
E. you can’t tell which interval is the 90, 95 or
99%, so you can’t say.
7. Let X∼N(12.4569,2.3425). Which of the fol-
lowing probabilities is the largest? (Note: you
don’t need to do any calculations!)
A. Pr(X= 18.2831)
B. Pr(X>11.4127)
C. Pr(X>15.2114)
D. Pr(X=4.5829)
E. Pr(X<10.5918)
8. Assume X∼N(15,32)andY∼N(5,42)and
that Xand Yare independent. What is the
approximate distribution of X25 −Y25 ?
A. N(10,52)
B. N(20,72)
C. N(10,−12)
D. N(10,72)
E. N(10,12)
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