Assignment- Inferences and Linear Regression

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

2. Which of the following statements are true regarding the simple linear regression model y_i = β₀ + β₁x_i + ε_i?
A. y_i is a value of the dependent variable (y) and x_i is a value of the independent variable (x).
B. β₀ is the slope of the regression line.
C. β₁ is the y-intercept of the regression line.
D. ε_i is a nonrandom error.

3. 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. normal
D. t-

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

5. 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.

6. 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¯₁ - x¯₂ if the
A. populations are at least normally distributed with equal variances.
B. populations are nonnormal with unequal variances.
C. ample sizes are both large.
D. sizes are both greater than 30.

7. 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. 13.120 and 40.647.
C. 39.364.
D. 12.401 and 39.364.

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

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

9. 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 plus the variation within the treatments.
C. between the treatments divided by the variation within the treatments.
D. within the treatments divided by the variation between the treatments.

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

11. 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.

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

13. Given the significance level 0.05, the F-value for the degrees of freedom, df = (3,7) is
A. 4.12.
B. 8.89.
C. 6.16.
D. 4.35.

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?
A. 4.96
B. 2.314
C. 0.897
D. 1.635

15. 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. 0.90.
B. 0.20.
C. 0.05.
D. 0.10.

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

A. determination equal to 1.
B. correlation of 0.
C. correlation equal to -1.
D. determination equal to -1.

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

18. 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.

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

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

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