STATS Exam: 250714RR – Inferences and Linear Regression (2015)

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Questions 1
to 20:Select the best answer to each question. Note that a question
and its answers may be split across a page break, so be sure that you have seen
the entire question and all the answers before choosing an
answer.

1. Another name for the residual term in a regression equation is
A. homoscedasticity.
B. random
error.
C. pooled
variances.
D. residual
analysis.

2. An indication of no linear relationship between two variables
would be a coefficient of
A. correlation
equal to ?1.
B. determination
equal to ?1.
C. determination
equal to 1.
D. correlation
of 0.

3. The object on which the response and factors are observed is
called
A. factor
level.
B. experimental
unit.
C. treatments.
D. factors.

4. In using the ANOVA models, the assumptions made about the data
are
A. the
population variances are equal.
B. the samples
are independent.
C. all 3
assumptions made here about the data.
D. the
population distributions are normal.

5.
Which of the following statements are true
regarding the simple linear regression model y = ? + ? x +
i 0 1 i?? i
A. y is a value of the dependent variable (y) and x is a value of the independent variable (x).i i
B. ?0 is the
slope of the regression line. C. ? is the y-intercept of the regression line.1
D. ?i is a nonrandom error.

6.
A random sample of males and females involved in rear-end accidents results in
the following Minitab summary:

N

MEAN

MEDIAN

TRMEAN

STDEV SEMEAN

FEMALES

33

23.91

20.00

23.38

9.77

1.70

MALES

38

28.87

28.50

28.44

9.67

1.57

What is the value of the test statistic
(Z score)?
A. 1.64
B. ?4.96
C. 2.32
D. ?2.14

7. A regression analysis between sales (in $1000) and advertising
(in $) resulted in the following least squares line: yˆ = 80,000 + 5x. This
implies that an increase of _______ in advertising is expected to result in an
increase of _______ in sales.
A. $1, $5,000
B. $1, $5
C. $1, $80,005
D. $5, $5,000

8. A chi-square test for independence with 8 degrees of freedom
results in a test statistic of 18.21. Using the chi-square table, the most accurate statement that can be made
about the p-value for this test is
that
A. 0.025 > p-value > 0.01.
B. 0.05 > p-value > 0.025.
C. p-value < 0.01. D. 0.10 > p-value > 0.05.

9.
In testing the difference between two population means using two independent
samples, we use the pooled variance in estimating the standard error of the
sampling distribution of the sample mean difference
x?
? x? if the
1 2
A. populations
are at least normally distributed with equal variances.
B. sizes are
both greater than 30.
C. populations
are nonnormal with unequal variances.
D. ample sizes
are both large.

10. Lily Energy Systems manufacturer’s wood-burning heaters and
fireplace inserts. One of its systems has an electric blower, which is thermostatically
controlled. The blower is designed to automatically turn on when the
temperature in the stove reaches 125°F and turn off at 85°F. Complaints from
customers indicate that the thermostat control is not working properly. The
company feels that the thermostat is acceptable if the variance in the cutoff
temperature is less than or equal to 175. The company takes a sample of 24
thermostats and finds that the variance equals 289. The calculated chi-square
test statistic and the table value for a 0.05 significance level are
A. 38.076,
38.99.
B. 37.983,
35.172.
C. 35.172,
38.99.
D. 37.983,
38.076.

11. In testing a population variance or constructing a confidence
interval for the population variance, an essential assumption is that
A. the
population is normally distributed.
B. expected
frequencies equal or exceed 5.
C. the
population is uniformly distributed.
D. sample size
exceeds 30.

12. Given the significance level 0.025, the F-value for the degrees of freedom, df = (7,3) is
A. 8.45.
B. 5.89.
C. 27.67.
D. 14.62.

13.
Consider the following data values of variables x and y.

x

4

2

6

4

3

y

5

3

7

6

5

Find the least squares regression
line.
A. ?1.045 +
0.932x
B. 1.122 +
1.073x
C. 1.659 +
0.932x
D. 21.206 +
1.073x

14.
A random sample of males and females involved in rear-end accidents results in
the following Minitab summary:

N
MEAN MEDIAN TRMEAN STDEV SEMEAN

FEMALES
33

23.91

20.00

23.38

9.77

1.70

MALES

38

28.87

28.50

28.44

9.67

1.57

What is the standard error of the
statistic between the two means?
A. 1.635
B. 0.897
C. 2.314
D. 4.96

15. A “best-fit” mathematical equation for the values of
two variables, x and y, is called
A. errors of
prediction.
B. regression
analysis.
C. correlation
analysis.
D. scatter
diagram.

16. In testing for the equality of two population variances, when
the populations are normally distributed, the 10% level of significance has
been used. To determine the rejection region, it will be necessary to refer to
the F table corresponding to an
upper-tail area of
A. 0.10.
B. 0.20.
C. 0.05.
D. 0.90.

17. The vertical distances between observed and predicted values of
y are called
A. least
square lines.
B. scatterplots.
C. errors of
prediction.
D. methods of
least squares.

18. A balanced experiment requires that
A. an equal
number of persons or test units receives each treatment.
B. at least
two treatment groups be used.
C. the number
of treatments equals the number of samples.
D. at least
one sample equal size is 30.

19. A left-tail area in the chi-square distribution equals 0.95.
For df = 10, the table value equals
A. 18.307.
B. 3.940.
C. 20.483.
D. 15.987.

20. With larger and larger numbers of categories in chi-square
tests, the chi-square distribution takes on the shape of the _______ distribution.
A. binomial
B. t-
C. Poisson
D. normal
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End of exam