Inferences and Linear

file-4

StudentID: 21317632

Exam: 250714RR – INFERENCES AND LINEAR REGRESSION

When you have completed your exam and reviewed your answers, click Submit Exam. Answers will not be recorded until you
hit Submit Exam. If you need to exit before completing the exam, click Cancel Exam.

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. Given the significance level 0.025, the F-value for the degrees of freedom, df = (7,3) is
A. 14.62.

B. 5.89.

C. 8.45.

D. 27.67.

2. 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

B. $5, $5,000

C. $1, $80,005

D. $1, $5,000

3. 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. correlation of 0.

D. determination equal to 1.

4. 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. sample size exceeds 30.

D. the population is uniformly distributed.

5. The object on which the response and factors are observed is called
A. treatments.

B. factors.

C. experimental unit.

D. factor level.

6. 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. 0.10 > p-value > 0.05.

C. p-value < 0.01.

D. 0.05 > p-value > 0.025.

7. A balanced experiment requires that
A. at least two treatment groups be used.

B. at least one sample equal size is 30.

C. an equal number of persons or test units receives each treatment.

D. the number of treatments equals the number of samples.

8. In a hypothesis test for the population variance, the alternate hypothesis is the population variance does
not equal 17.0. The significance level to be used is 0.05 and the sample size to be taken is 25. The table
value(s) to use from the chi-square distribution is/are
A. 12.401 and 39.364.

B. 39.364.

C. 13.120 and 40.647.

D. 40.647.

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

What is the standard error of the statistic between the two means?

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

A. 0.897

B. 2.314

C. 1.635

D. 4.96

10. Another name for the residual term in a regression equation is
A. pooled variances.

B. random error.

C. homoscedasticity.

D. residual analysis.

11. 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. normal

C. t-

D. Poisson

12. What is the slope of the line that passes through the points (−5, −8) and (3,8)?
A. −½
B. ½

C. 2

D. −2

13. 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. 0.05.

C. 0.90.

D. 0.20.

14. A “best-fit” mathematical equation for the values of two variables, x and y, is called
A. scatter diagram.

B. regression analysis.

C. errors of prediction.

D. correlation analysis.

15. In using the ANOVA models, the assumptions made about the data are
A. the samples are independent.

B. A, B, and C are all assumptions made about the data.

C. the population distributions are normal.

D. the population variances are equal.

16. Which of the following statements are true regarding the simple linear regression model y
i
= β

0
+ β

1
x

i
+

ε
i
?

A. ε
i
is a nonrandom error.

B. β1 is the y-intercept of the regression line.

C. β
0
is the slope of the regression line.

D. yi is a value of the dependent variable (y) and xi is a value of the independent variable (x).

17. A left-tail area in the chi-square distribution equals 0.95. For df = 10, the table value equals
A. 3.940.

B. 15.987.

C. 18.307.

End of exam

D. 20.483.

18. In testing the difference between two population means using two independent samples, the sampling
distribution of the sample mean difference x̄1 − x̄2 is normal if the

A. population sizes are both greater than 30.

B. populations are normal.

C. sizes are both greater than 30.

D. populations are nonnormal and the sample sizes are large.

19. 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. 37.983, 38.076.

B. 37.983, 35.172.

C. 35.172, 38.99.

D. 38.076, 38.99.

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

Find the least squares regression line.

x 4 2 6 4 3

y 5 3 7 6 5

A. 1.659 + 0.932x

B. 21.206 + 1.073x

C. −1.045 + 0.932x
D. 1.122 + 1.073x