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Exam: inferences and linear regression

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1. 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. 40.647.

B. 39.364.

C. 12.401 and 39.364.

D. 13.120 and 40.647.

2. The vertical distances between observed and predicted values of y are called

A. methods of least squares.

B. errors of prediction.

C. least square lines.

D. scatterplots.

3. 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. 0.05.

B. 0.10.

C. 0.20.

D. 0.90.

4. 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

x̄1

− x̄2

if the

A. ample sizes are both large.

B. sizes are both greater than 30.

C. populations are at least normally distributed with equal variances.

D. populations are nonnormal with unequal variances.

5. 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. 4.96

B. 1.635

C. 0.897

D. 2.314

6. A balanced experiment requires that

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

B. the number of treatments equals the number of samples.

C. at least one sample equal size is 30.

D. at least two treatment groups be used.

7. An indication of no linear relationship between two variables would be a coefficient of

A. determination equal to 1.

B. determination equal to −1.

C. correlation equal to −1.

D. correlation of 0.

8. 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. 38.076, 38.99.

D. 35.172, 38.99.

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

A. 5.89.

B. 27.67.

C. 8.45.

D. 14.62.

10. The object on which the response and factors are observed is called

A. treatments.

B. experimental unit.C. factor level.

D. factors.

11. The F-statistic in a one-way ANOVA represents the variation

A. within the treatments minus the variation between the treatments.

B. between the treatments divided by the variation within the treatments.

C. within the treatments divided by the variation between the treatments.

D. between the treatments plus the variation within the treatments.

12. In testing a population variance or constructing a confidence interval for the population variance, an

essential assumption is that

A. expected frequencies equal or exceed 5.

B. the population is normally distributed.

C. the population is uniformly distributed.

D. sample size exceeds 30.

13. Which of the following statements are true regarding the simple linear regression model y

i

= β

0

+ β

1

x

i

+

ε

i

?

A. β

0

is the slope of the regression line.

B. ε

i

is a nonrandom error.

C. y

i

is a value of the dependent variable (y) and x

i

is a value of the independent variable (x).

D. β

1

is the y-intercept of the regression line.

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

A. 15.987.

B. 18.307.

C. 3.940.

D. 20.483.

15. Another name for the residual term in a regression equation is

A. homoscedasticity.

B. pooled variances.

C. residual analysis.

D. random error.

16. 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 1.57End of exam

What is the value of the test statistic (Z score)?

A. 1.64

B. 2.32

C. −2.14

D. −4.96

17. In using the ANOVA models, the assumptions made about the data are

A. the samples are independent.

B. all 3 assumptions made here about the data.

C. the population variances are equal.

D. the population distributions are normal.

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

A. ½

B. 2

C. −2

D. −½

19. 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. 1.122 + 1.073x

B. 1.659 + 0.932x

C. −1.045 + 0.932x

D. 21.206 + 1.073x

20. 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 nonnormal and the sample sizes are large.

C. sizes are both greater than 30.

D. populations are normal.

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