Chapter 24–Statistical inference: Conclusion
MULTIPLE CHOICE
1. For a sample of size 18 taken from a normally distributed population with standard deviation equal to
5, a 95% confidence interval for the population mean would require:
A.
z = 1.960.
B.
z = 1.645.
C.
t = 2.110.
D.
t = 1.740.
2. In a chi-squared test of a contingency table, the value of the test statistic was 2 = 10.5, and the
critical value at α = .05 was 15.507 Thus we:
A.
fail to reject the null hypothesis at α = 0.05.
B.
reject the null hypothesis at α = 0.05.
C.
don’t have enough evidence to accept or reject the null hypothesis at α = 0.05.
D.
should decrease the level of significance in order to reject the null hypothesis.
3. Given the least squares regression line = –5.33 + 1.52x, and a coefficient of determination of 0.964,
the coefficient of correlation is:
A.
–0.929.
B.
0.929.
C.
–0.982.
D.
0.982.
4. A random sample of size 20 taken from a normally distributed population resulted in a sample
variance of 50. The lower limit of a 95% confidence interval for the population variance would be:
A.
106.663.
B.
93.901.
C.
31.516.
D.
28.917.
5. In a multiple regression analysis involving 35 observations and 5 independent variables,
SSy = 380 and SSR = 320. The multiple coefficient of determination adjusted for degrees of freedom
is:
A.
0.808.
B.
0.815.
C.
0.013.
D.
−0.023.
6. In a Kruskal–Wallis test for comparing four populations, the test statistic is calculated as H = 8.64. If
the test is conducted at the 5% significance level, then the:
A.
null hypothesis will be rejected.
B.
null hypothesis will not be rejected.
C.
test results are inconclusive.
D.
t-test for matched pairs must be used.
7. In a multiple regression analysis involving 35 observations and 5 independent variables SSR = 320 and
SSE = 60. The standard error of estimate is:
A.
2.322.
B.
1.464.
C.
1.438.
D.
3.381.
8. Consider the following ANOVA table:
Source of
variation
SS
df
MS
F
Treatments
12
3
4.0
2.667
Error
18
12
1.5
Total
30
15
The number of treatments is:
A.
30.
B.
4.
C.
3.
D.
15.
9. In a regression model involving 50 observations, the estimated regression model obtained was
= 9.5 + 2.3x1 + 4.7x2 + 5.8x2. For this model, SSR = 750 and SSE = 225. The value of MSR is:
A.
75.
B.
525.
C.
250.
D.
There is not enough information to answer this question.
10. In testing whether the means of two normal populations are equal, summary statistics computed for
two independent samples are as follows:
n1 = 30, x1 = 6.25, s1 = 1.15
n2 = 20, x2 = 5.75, s2 = 1.25
Assume that the population variances are equal. Then the standard error of the sampling distribution of
the sample mean difference 1 – 2 is equal to:
A.
0.3437.
B.
0.3320.
C.
0.3608.
D.
0.3496.
11. In a randomised block design for ANOVA, the number of treatments is 5, the number of observations
n = 20, and the number of blocks is 4. The number of degrees of freedom for error is:
A.
4.
B.
3.
C.
12.
D.
19.
12. In testing the difference between two population means using two independent samples, the population
standard deviations are assumed to be known and the calculated test statistic equals 2.98. If the test is
two-tailed and the 10% level of significance has been specified, the conclusion should be:
A.
to reject the null hypothesis.
B.
not to reject the null hypothesis.
C.
to choose two other independent samples.
D.
None of the above answers is correct.
13. If the coefficient of determination is 1, then the slope of the regression line:
A.
must be 1.
B.
must be −1.
C.
must be 0.
D.
None of the above answers is correct.
14. Suppose that the sample regression equation of a second-order model is = 1.50 + 0.30x + 0.40x2. The
value 1.50 is the:
A.
intercept where the response surface strikes the y-axis.
B.
intercept where the response surface strikes the x-axis.
C.
predicted value of y.
D.
predicted value of y when x = 1.
15. If the coefficient of correlation is 0.80, the percentage of the variation in the dependent variable y that
is explained by the variation in the independent variable x is:
A.
80%.
B.
64%.
C.
–0.80%
D.
0.64%.
16. In constructing a 95% interval estimate for the ratio of two population variances, , two
independent samples of sizes 25 and 30 are drawn from the populations. If the sample variances are
620 and 880, then the upper confidence limit is:
A.
1.566.
B.
1.562.
C.
1.597.
D.
1.518.
17. A random sample of size 15 taken from a normally distributed population revealed a sample mean of
80 and a sample variance of 16. The upper limit of a 90% confidence interval for the population mean
would equal:
A.
81.819.
B.
78.301.
C.
78.181.
D.
81.699.
18. A multiple regression model involves 4 independent variables and 25 observations. If we want to test
at the 10 percent significance level the parameter β3, the critical value is:
A.
2.528.
B.
1.721.
C.
1.725.
D.
2.518.
19. The upper limit of a confidence interval at the 90% level of confidence for the population proportion if
a sample of size 200 had 50 successes is:
A.
0.1996.
B.
0.3004.
C.
0.2515.
D.
0.2485.
20. The regression line = 5 + 2x has been fitted to the data points (5,13), (3,10), and (4,11). The sum of
the squared residuals will be:
A.
11.
B.
15.
C.
7.
D.
9.
21. In a one-way ANOVA where there are 3 treatments and 32 observations, the degrees of freedom for
the F-statistic are equal to:
A.
29 and 2.
B.
2 and 29.
C.
2 and 28.
D.
28 and 2.
22. Suppose that we want to model the randomised block design of the analysis of variance with, say, five
treatments and three blocks. We would create:
A.
8 indicator variables.
B.
7 indicator variables.
C.
6 indicator variables.
D.
5 indicator variables.
23. Consider the following two samples:
A:
10
12
13
B:
9
11
14
14
15
17
18
The value of the test statistic for a right-tail Wilcoxon rank sum test is:
A.
4.
B.
7.
C.
19.5.
D.
46.5.
24. One-way ANOVA is performed on independent samples taken from three normally distributed
populations with equal variances. The following summary statistics are calculated:
n1 = 5, x1 = 60, s1 = 4.8
n2 = 8, x2 = 65, s2 = 4.2
n3 = 7, x3 = 57, s3 = 5.1
The grand mean equals:
A.
60.95.
B.
60.67.
C.
62.50.
D.
58.50.
25. Two samples of sizes 20 and 25 are independently drawn from two normal populations, where the
unknown population variances are assumed to be equal. The number of degrees of freedom of the
equal-variances t-test statistic is:
A.
45.
B.
44.
C.
43.
D.
25.
26. In a normal approximation to the Wilcoxon rank sum test, the standardised test statistic is calculated as
z = 2.28. For a two-tail test, the p-value is:
A.
0.4887.
B.
0.0226.
C.
0.0113.
D.
0.9774.
27. In a regression problem, the following pairs of (x, y) are given: (5, 1), (5, –1), (5, 0), (5, –2) and (5, 2).
This indicates that the:
A.
correlation coefficient is –1.
B.
correlation coefficient is 0.
C.
correlation coefficient is 1.
D.
coefficient of determination is between –1 and 1.
28. In testing the utility of a multiple regression model involving 3 independent variables and 57
observations, the numbers of degrees of freedom for the numerator and denominator, respectively, for
the critical value of F will be:
A.
2 and 53.
B.
3 and 53.
C.
2 and 54.
D.
3 and 54.
29. A Wilcoxon rank sum test for comparing two populations involves two independent samples of sizes 4
and 6. The alternative hypothesis is stated as: The location of population 1 is different from the
location of population 2. The appropriate critical values at the 10% significance level are:
A.
14, 30.
B.
25, 41.
C.
12, 32.
D.
23, 43.
30. In a multiple regression analysis involving 35 data points, the standard error of estimate squared is
calculated as = 1.6 and the sum of squares for error as SSE = 48. The number of independent
variables must be:
A.
3.
B.
4.
C.
5.
D.
6.
31. A sample of size 200 from population 1 has 80 successes. A sample of size 150 from population 2 has
48 successes. The value of the test statistic for testing the null hypothesis that the proportion of
successes in population one exceeds the proportion of successes in population two by 0.02 is:
A.
1.400.
B.
1.320.
C.
1.166.
D.
1.667.
32. One-way ANOVA is applied to independent samples taken from three normally distributed
populations with equal variances. The following summary statistics are calculated:
n1 = 8, x1 = 50, s1 = 4.
n2 = 10, x2 = 58, s2 = 5.
n3 = 15, x3 = 52, s3 = 3.5.
The between-treatments variation equals:
A.
508.50.
B.
166.67.
C.
16.95.
D.
333.33.
33. Which of the following statements is correct regarding the percentile points of the F-distribution?
A.
F.10, 5, 8 = 1 / F.90, 5, 8
B.
F.10, 5, 8 = 1 / F.00, 8, 5
C.
F.90, 5, 8 = 1 / F.90, 8, 5
D.
F.90, 5, 8 = 1 / F.10, 8, 5
34. Consider the following ANOVA table:
Source of
variation
SS
df
MS
F
Treatments
192
4
48
1.778
Error
405
15
27
Total
597
19
The number of observations in all samples is:
A.
15.
B.
19.
C.
20.
D.
27.
35. If cov (X, Y) = 1450, = 1800 and = 1300, then the coefficient of determination R2 is:
A.
0.8056.
B.
0.4677.
C.
0.8985.
D.
0.7222.
36. The number of degrees of freedom in a test of a contingency table with 6 rows and 4 columns equals:
A.
15.
B.
18.
C.
20.
D.
24.
37. For the regression equation = 60 + 8x1 – 6x2 – 4x1x2, a unit increase in x2 holding x1 constant at a
value of 3, decreases the value of y on average by:
A.
66.
B.
18.
C.
42.
D.
an amount that depends on the value of x2.
38. Suppose that a one-tail t-test is being applied to find out if the population mean is less than 200. The
level of significance is 0.10 and 20 observations were sampled. The rejection region is:
A.
t > 1.729.
B.
t < –1.328.
C.
t > 1.725.
D.
t < –1.325.
39. The degrees of freedom in a chi-squared test for normality, where the number of standardised intervals
is 6 and there are 2 population parameters to be estimated from the data, is equal to:
A.
6.
B.
4.
C.
3.
D.
2.
40. In one-way ANOVA, suppose that there are five treatments with n1 = n2 = n3 = 9, and n4 = n5 = 10.
Then the mean squares for error, MSE, equals:
A.
SSE / 4.
B.
SSE / 46.
C.
SSE / 43.
D.
SSE / 42.
41. Consider a multinomial experiment with 120 trials, where the outcome of each trial can be classified
into one of 6 categories. The number of degrees of freedom associated with the chi-squared goodness-
of-fit test equals:
A.
114.
B.
126.
C.
119.
D.
5.
42. The Wilcoxon rank sum test statistic T is approximately normally distributed whenever the sample
sizes are larger than:
A.
10.
B.
15.
C.
20.
D.
30.
43. One-way ANOVA is applied to independent samples taken from three normally distributed
populations with equal variances. The following summary statistics are calculated:
n1 = 6, x1 = 13, s1 = 3.
n2 = 8, x2 = 16, s2 = 4.
n3 = 5, x3 = 18, s3 = 2.
The within-treatments variation equals:
A.
202.
B.
173.
C.
139.
D.
29.
44. Based on sample data, the 95% confidence interval limits for the population mean are
LCL = 189.11, UCL = 207.36.
If the 5% level of significance were used in testing the hypotheses.
H0 : μ = 200.
H1 : μ 200.
the null hypothesis:
A.
would be rejected.
B.
would not be rejected.
C.
would have to be revised.
D.
None of the above answers is correct.
45. In testing for the equality of two population variances, when the populations are normally distributed,
the 5% 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.
0.95.
B.
0.025.
C.
0.10.
D.
0.05.
46. A chi-squared test of a contingency table with 3 rows and 5 columns shows that the value of the test
statistic is 18.963. The most accurate statement that can be made about the p-value for this test is that:
A.
p-value is greater than 0.05.
B.
p-value is greater than 0.025.
C.
p-value is greater than .010 but smaller than 0.025.
D.
p-value is greater than 0.10.
47. When the necessary conditions are met, a two-tail test is being conducted to test the difference
between two population proportions. If the value of the test statistic z is 1.73, then the p-value is:
A.
0.4582.
B.
0.0836.
C.
0.2291.
D.
0.0418.
48. In sign test applications, the normal approximation to the binomial distribution may be used whenever
the number of nonzero differences is greater than or equal to:
A.
5.
B.
10.
C.
15.
D.
20.
49. When the necessary conditions are met, a two-tail test is being conducted to test that the difference
between two population proportions is zero. The two sample proportions are 1 = 0.18 and 2 = 0.15,
and the standard error of the sampling distribution of 1 – 2 is 0.02. The calculated value of the test
statistic will be:
A.
z = 0.21.
B.
t = 0.21.
C.
z = 1.50.
D.
t = 1.50.
50. In a multiple regression analysis, there are 25 data points and 4 independent variables, and the sum of
the squared differences between observed and predicted values of y is 200. The multiple standard error
of estimate will be:
A.
10.00.
B.
3.162.
C.
8.0.
D.
10.0.
51. In a Kruskal–Wallis test at the 5% significance level, there are five samples and the value of the test
statistic is calculated as H = 10.27. The most accurate statement that can be made about the p-value is
that it is:
A.
greater than 0.10.
B.
greater than 0.05 but smaller than 0.10.
C.
greater than 0.05.
D.
greater than 0.025 but smaller than 0.05.
52. In a multiple regression analysis involving 30 observations and 4 independent variables, SSY = 250
and SSE = 40. The multiple coefficient of determination is:
A.
0.917.
B.
0.840.
C.
0.862.
D.
0.928.
53. In order to represent a qualitative independent variable that has five possible categories, we must
create:
A.
6 indicator variables.
B.
5 indicator variables.
C.
4 indicator variables.
D.
3 indicator variables.
54. In order to test the utility of a multiple regression model involving 4 independent variables and 25
observations, the number of degrees of freedom for the numerator and denominator, respectively, for
the critical value of F are:
A.
4 and 25.
B.
5 and 24.
C.
4 and 20.
D.
3 and 20.
55. A random sample of 28 observations is selected from a normally distributed population. The sample
variance is 12.96. In the 95% confidence interval for the population variance, the upper limit will be:
A.
24.011.
B.
21.665.
C.
8.723.
D.
8.101.
56. When the necessary conditions are met, a two-tail test is being conducted to test the difference
between two population means, but your statistical software provides only a one-tail area of 0.042 as
part of its output. The p–value for this test will be:
A.
0.021.
B.
0.479.
C.
0.084.
D.
0.958.
57. In a sign test, the following information is given: number of zero differences = 2, number of positive
differences = 18, and number of negative differences = 7. The value of the standardised test statistic is:
A.
9.0.
B.
3.5.
C.
2.2.
D.
2.0.
58. In testing the hypotheses
H0 : μ = 100.
H1 : μ < 100.
the sample mean is found to be 58. The null hypothesis:
A.
should be rejected.
B.
should not be rejected.
C.
should be rejected only if n > 30.
D.
None of the above answers is correct.
59. A matched pairs experiment yielded the following paired differences:
4
–2
3
3
3
–2
0
2
0
2
4
0
–1
3
–1
4
3
2
3
0
The value of the standardised sign test statistic is:
A.
12.
B.
8.
C.
4.
D.
2.
60. A multiple regression model involves 6 independent variables and 25 observations. If we want to test
at the significance level the parameter β3, the critical value is:
A.
1.734.
B.
1.330.
C.
2.740.
D.
1.729.
61. From a sample of 200 items, 18 are defective. The point estimate of the population proportion of non-
defective items will be:
A.
182.
B.
0.91.
C.
18.
D.
0.09.
62. For the regression equation = 10 + 5x1 + 4x2 + 3x1x2, a unit increase in x1 increases the value of y on
average by:
A.
4.
B.
22.
C.
19.
D.
an amount that depends on the value of x2.
63. In a Friedman test for comparing three populations, provided that there six blocks, the test statistic is
calculated as F = 6.75. If the test is conducted at the 10% significance level, the conclusion and p–
value will be:
A.
reject the null hypothesis, and 0.025 < p-value < 0.050.
B.
reject the null hypothesis, and p-value > 0.050.
C.
do not reject the null hypothesis, and 0.025 < p-value < 0.050.
D.
do not reject the null hypothesis, and p-value > 0.05.
64. The number of degrees of freedom associated with the t-test, when the data are gathered from a
matched pairs experiment with eight pairs, is:
A.
8.
B.
16.
C.
7.
D.
14.
65. In a simple linear regression model, the standard error of estimate sE = 15 and n = 8. The sum of
squares for error, SSE, is:
A.
225.
B.
1350.
C.
1800.
D.
120.
66. The number of degrees of freedom for a contingency table with 3 rows and 5 columns is:
A.
15.
B.
3.
C.
8.
D.
5.
67. In testing the hypotheses:
H0: p = 0.20.
H1: p > 0.20.
at the 5% significance level, if the sample proportion is 0.25, and the standard error of the sample
proportion is 0.025, the appropriate conclusion would be:
A.
to reject H0.
B.
not to reject H0.
C.
to reject H1.
D.
to reject both H0 and H1.
68. Consider the following two samples:
A:
17
18
20
23
35
B:
28
32
35
38
40
The value of the test statistic for a left-tail Wilcoxon rank sum test is:
A.
10.0.
B.
17.5.
C.
37.5.
D.
20.0.
69. If the coefficient of correlation is –0.90, the percentage of the variation in y that is explained by the
variation in x is:
A.
90%.
B.
81%.
C.
–90%.
D.
–81%.
70. For the regression equation = 15 – 10x1 + 5x2 + 3x1x2, a unit increase in x1, holding x2 constant at a
value of 2, decreases the value of y on average by:
A.
4.
B.
7.
C.
10.
D.
an amount that depends on the value of x1.
71. In a simple linear regression analysis, the following statistics are given:
= 400, = 600, cov(X, Y) = 80, n = 5.
The standard error of estimate is:
A.
10.954.
B.
48.332.
C.
27.905.
D.
12.500.
72. The significance level for a Wilcoxon signed rank sum test is 0.05. The alternative hypothesis is stated
as: The location of population 1 is to the left of the location of population 2. The appropriate critical
value for a sample of size 15 (that is, the number of nonzero differences) is:
A.
90.
B.
25.
C.
30.
D.
95.
73. In a hypothesis test for the population variance, the hypotheses are:
H0 : σ 2 = 84.
H1 : σ 2 84.
If the sample size is 20 and the test is being carried out at the 10% level of significance, the rejection
region will be:
A.
2 < 10.117 or 2 > 30.114.
B.
2 < 11.651 or 2 > 27.204.
C.
2 < 9.390 or 2 > 28.869.
D.
2 < 10.850 or 2 > 31.410.
74. One-way ANOVA is performed on three independent samples with n1 = 5, n2 = 6 and n3 = 7. The
critical value obtained from the F table for this test at the 5% level of significance equals:
A.
4.77.
B.
19.43.
C.
3.68.
D.
39.43.
75. If the coefficient of correlation is –0.70, then the coefficient of determination is:
A.
–0.70.
B.
–0.49.
C.
0.49.
D.
0.30.
76. In a completely randomised design for ANOVA, the number of degrees of freedom for the numerator
and denominator are 3 and 18, respectively. The total number of observations must equal:
A.
18.
B.
21.
C.
22.
D.
17.
77. For a multiple regression model, the following statistics are given:
total variation in y = SSY = 800, SSE = 120, n = 25.
The multiple coefficient of determination is:
A.
0.850.
B.
0.150.
C.
0.208.
D.
0.031.
78. For a multiple regression model the following statistics are given:
SSE = 75, SSY = 300, k = 5, n = 25.
The coefficient of determination adjusted for degrees of freedom is:
A.
0.750.
B.
0.684.
C.
0.866.
D.
0.829.
79. In the least squares regression line = 3 – 2x, the predicted value of y equals:
A.
0 when x = –1.5.
B.
2 when x = 2.
C.
2 when x = –2.
D.
0 when x = 1.5.
80. A multiple regression model has the form = 8.5 + 3x1 + 5x2. As x2 increases by 1 unit, holding x1
constant, the value of y will increase by:
A.
3 units.
B.
8.5 units.
C.
5 units on average.
D.
None of the above answers is correct.
81. In a Wilcoxon signed rank sum test for matched pairs with n = 32, the rank sums of the positive and
negative differences are 367.5 and 160.5, respectively. The value of the standardised test statistic is:
A.
5.016.
B.
1.935.
C.
2.290.
D.
2.240.
82. For the multiple regression model = 5 – 4x1 + 3x2 + 2x3, a unit increase in x1, holding x2 and x3
constant, results in:
A.
an increase of 4 units in the value of y.
B.
a decrease of 4 units in the value of y.
C.
a decrease of 4 units on average in the value of y.
D.
an increase of 6 units in the value of y.
83. The largest value that the standard error of estimate s
can assume is:
A.
−1.
B.
1.
C.
0.
D.
None of the above answers is correct.
84. A randomised block design with 5 treatments and 3 blocks produced the following sum of squares
values: SS(Total) = 1558, SST = 262, SSE = 200. The value of SSB must be:
A.
1296.
B.
1096.
C.
1358.
D.
470.
85. In multiple regression analysis involving 8 independent variables and 80 observations, the critical
value of t for testing individual coefficients in the model will have:
A.
80 degrees of freedom.
B.
8 degrees of freedom.
C.
71 degrees of freedom.
D.
7 degrees of freedom.
86. In a normal approximation to the sign test, the standardised test statistic is calculated as z = 1.06. To
test the alternative hypothesis that the location of population 1 is to right of the location of population
2, the p-value is:
A.
0.2892.
B.
0.3554.
C.
0.1446.
D.
0.0723.
87. In a regression model involving 50 observations, the estimated regression model obtained was
= 38.7 + 0.56x1 + 0.72x2 – 0.24x3. For this model SSY = 86 765 and SSR = 20 152. The value of
MSE is:
A.
1448.109.
B.
7798.824.
C.
4836.480.
D.
9676.333.
88. Given that the sum of squares for error is 45 and the sum of squares for regression is 175, the
coefficient of determination is:
A.
1.972.
B.
0.257.
C.
0.795.
D.
0.205.
89. A multiple regression equation includes 4 independent variables, and the coefficient of multiple
determination is 0.96. The percentage of the variation in y that is explained by the regression equation
is:
A.
4%.
B.
96%.
C.
24%.
D.
32%.
90. In a Wilcoxon signed rank sum test, the test statistic is calculated as T = 132. If there are n = 20
observations for which D 0, and a two-tail test is performed at the 5% significance level, therefore:
A.
we reject the null hypothesis.
B.
we do not reject the null hypothesis.
C.
the test results are inconclusive.
D.
we perform a parametric test.
91. In a normal approximation to the Wilcoxon signed rank test, the test statistic is calculated as
z = 0.88. For a two-tail test, the p-value is:
A.
0.3788.
B.
0.3800.
C.
0.1894.
D.
0.0947.
92. In order to estimate with 90% confidence the expected value of y in a simple linear regression
problem, a random sample of 15 observations is taken. Which of the following t-table values listed
below would be used?
A.
1.350
B.
1.771
C.
1.753
D.
1.341
93. In a multiple regression analysis involving 6 independent variables and 62 data points, the sums of
squares are calculated as SSR = 900 and SSE = 300. The value of the F-test statistic for this model is:
A.
3.06.
B.
33.60.
C.
27.50.
D.
3.73.
94. Given the data points (X, Y) = (2, 2), (3, 3), (4, 4), (5, 5) and (6, 6), the least squares estimates of the y–
intercept and the slope are respectively:
A.
0 and 1.
B.
–1 and 0.
C.
4 and 4.
D.
4 and 0.
95. In a multiple regression analysis involving 8 independent variables and 40 data points, the number of
degrees of freedom associated with the sum of squares for error is:
A.
7.
B.
32.
C.
39.
D.
31.
96. A sample of size 100 selected from one population has 70 successes, and a sample of size 200 selected
from a second population has 120 successes. The test statistic for testing the equality of the population
proportions is equal to:
A.
1.694.
B.
0.8367.
C.
0.7746.
D.
0.7958.
97. Suppose that the estimated regression equation of 400 business graduates is:
= 28,000 + 2600x + 1000I, where y is the starting salary, x is the grade point average and I is an
indicator variable that takes the value 1 if the student is a marketing major and 0 if not. A finance
major graduate with a 3.8 grade point average would have an average starting salary of:
A.
$31 800.
B.
$34 400.
C.
$38 880.
D.
$37 880.
98. In testing the hypotheses:
H0: ps = 0
H1: ps 0,
the Spearman rank correlation coefficient in a sample of 82 observations is 0.452. The value of the test
statistic is:
A.
6.051.
B.
54.457.
C.
4.068.
D.
4.093.
99. For the regression equation = 10 + 5x1 + 3x2, a unit increase in x2 increases the value of y on average
by:
A.
3.
B.
8.
C.
18.
D.
an amount that depends on the value of x1.
100. In a regression model involving 30 observations, the following estimated regression model was
obtained:
= 48 + 25x1 + 1.4x2 – x3.
For this model, SSY = 2020 and SSE = 520. The value of the F-statistic for testing the utility of this
model is:
A.
10.83.
B.
25.00.
C.
50.90.
D.
3.88.
101. In a simple linear regression analysis, the estimated regression line has a y-intercept of 8 and a slope of
4. When x = 2, the actual value of y is:
A.
8.
B.
4.
C.
2.
D.
unknown.
102. A multiple regression analysis that includes 5 independent variables results in a sum of squares for
regression of 1580 and a sum of squares for error of 420. The multiple coefficient of determination
will be:
A.
0.16.
B.
0.79.
C.
0.84.
D.
0.21.
103. A regression analysis between sales (in thousands of dollars) and advertising (in hundreds of dollars)
resulted in the least squares line = 80 + 5x. This implies that if advertising is $600, then the predicted
amount of sales (in dollars) is:
A.
$83 000.
B.
$110 000.
C.
$300 075.
D.
$3080.
SHORT ANSWER
1. A statistician kept track of the weight losses of ten people who were assigned diet A and the weight
losses of another ten people who were assigned diet B. These results are shown in the following table.
Weight losses
Diet A
Diet B
6
7
8
9
5
12
7
8
9
11
4
9
6
8
8
10
9
7
8
9
If we assume that the weight losses are normally distributed, can we conclude at the 5% significance
level that diet B is more effective than diet A?
2. A statistician kept track of the weight losses of ten people who were assigned diet A and the weight
losses of another ten people who were assigned diet B. These results are shown in the following
table.
Weight losses
Diet A
Diet B
6
7
8
9
5
12
7
8
9
11
4
9
6
8
8
10
9
7
8
9
a. Aside from the assumption of normality, what other assumption must you make in order to answer
the previous question?
b. Test to determine if that assumption is violated. Use = 0.10.