BUS714 Inferences and Linear Regression | Complete Solution

Exam: 250714RR - Inferences and Linear Regression

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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.    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 nonnormal with unequal variances.
D.    populations are at least normally distributed with equal variances.

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

3.    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.

4.    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. $5, $5,000
B. $1, $5
C. $1, $80,005
D. $1, $5,000

5.    With larger and larger numbers of categories in chi-square tests, the chi-square distribution takes on the shape of the     distribution.
A.    normal
B.    binomial
 
C.    Poisson
D.    t-

6.    The F-statistic in a one-way ANOVA represents the   variation
A.    between the treatments plus the variation within the treatments.
B.    within the treatments minus the variation between the treatments.
C.    within the treatments divided by the variation between the treatments.
D.    between the treatments divided by the variation within the treatments.

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

8.    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.

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

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

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

12.    The object on which the response and factors are observed is called
A.    factor level.
 
B.    experimental unit.
C.    treatments.
D.    factors.

13.    What is the slope of the line that passes through the points (−5, −8) and (3,8)?
A.    −½
B.    −2
C.    ½
D.    2

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

15.    A balanced experiment requires that
A.    at least one sample equal size is 30.
B.    an equal number of persons or test units receives each treatment.
C.    at least two treatment groups be used.
D.    the number of treatments equals the number of samples.

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
38    23.91    20.00    23.38    9.77    1.70
MALES        28.87    28.50    28.44    9.67    1.57

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

17.    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. 0.10.
D. 0.05.
 
18.    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. 0.10 > p-value > 0.05.
B. 0.05 > p-value > 0.025.
C. 0.025 > p-value > 0.01.
D. p-value < 0.01.

19.    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.    sizes are both greater than 30.
B.    populations are nonnormal and the sample sizes are large.
C.    populations are normal.
D.    population sizes are both greater than 30.

20.    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. 21.206 + 1.073x B. 1.122 + 1.073x C. 1.659 + 0.932x D. −1.045 + 0.932x