# Statistics for Business and Economics

1. 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. âˆ’1.045 + 0.932x

B. 1.122 + 1.073x

C. 1.659 + 0.932x

D. 21.206 + 1.073x

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

 N MEAN MEDIAN TREMEAN 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. âˆ’4.96

B. 2.32

C. âˆ’2.14

D. 1.64

3. A regression analysis between sales (in \$1000) and advertising (in \$) resulted in the following least squares line: yË† = 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, \$80,005

C. \$1, \$5

D. \$5, \$5,000

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

A. residual analysis.

B. homoscedasticity.

C. pooled variances.

D. random error.

5. In testing a population variance or constructing a confidence interval for the population variance, an essential assumption is that

A. sample size exceeds 30.

B. expected frequencies equal or exceed 5.

C. the population is normally distributed.

D. the population is uniformly distributed.

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

A. 15.987.

B. 3.940.

C. 18.307.

D. 20.483.

7. 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 xÌ„1 âˆ’ xÌ„2 if the

A. populations are nonnormal with unequal variances.

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

C. ample sizes are both large.

D. sizes are both greater than 30.

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

A. the population variances are equal.

B. the samples are independent.

D. the population distributions are normal.

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

A. treatments.

B. factor level.

C. factors.

D. experimental unit.

10. In testing the difference between two population means using two independent samples, the sampling distribution of the sample mean difference xÌ„1 âˆ’ xÌ„2 is normal if the

A. sizes are both greater than 30.

B. populations are normal.

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

D. population sizes are both greater than 30.

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

A. errors of prediction.

B. regression analysis.

C. scatter diagram.

D. correlation analysis.

12. 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 125Â°F and turn off at 85Â°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. 35.172, 38.99.

B. 37.983, 38.076.

C. 37.983, 35.172.

D. 38.076, 38.99.

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

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

B. between the treatments plus the variation within the treatments.

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

D. within the treatments minus the variation between the treatments.

14. 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 TREMEAN 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

15. What is the slope of the line that passes through the points (âˆ’5, âˆ’8) and (3,8)? A. 2 B. âˆ’2 C. Â½ D. âˆ’Â½

16. 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. 0.05 > p-value > 0.025.

B. p-value < 0.01.

C. 0.10 > p-value > 0.05.

D. 0.025 > p-value > 0.01.

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

A. 8.45.

B. 14.62.

C. 27.67.

D. 5.89.

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

= Î²0 + Î²1xi + Îµi?

A. Î²1 is the y-intercept of the regression line.

B. Î²0 is the slope of the regression line.

C. y i is a value of the dependent variable (y) and x is a value of the independent variable (x).

D. Îµi is a nonrandom error.

19. Given the significance level 0.05, the F-value for the degrees of freedom, df = (3,7) is

A. 4.35.

B. 8.89.

C. 4.12.

D. 6.16.

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. Poisson

C. t

D. normal