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

End of exam