Statistical Analysis II – Set # 1
Question 1 of 40
The statistic for the F distribution:
A. is always positive.
B. is always between 0 and 1.
C. is determined by the degrees of freedom in the denominator and the degrees of freedom in
the numerator.
D. Both A and C
Question 2 of 40
The mean rate of return on portfolio A (12 stocks) was calculated to be 11% with a standard
deviation of 3.4%. The mean rate of return on portfolio B (10 stocks) was determined to be
12.8% with a standard deviation of 4%. At the .05 significance level:
A. F = 3.02; we can conclude that there is more variation in portfolio B's performance.
B. F = 1.38; we cannot conclude that there is more variation in portfolio B's performance.
C. F = 3.02; we cannot conclude that there is more variation in portfolio B's performance.
D. F = 0.62; we cannot conclude that there is more variation in portfolio B's performance.
Question 3 of 40
To conduct an experiment comparing more than two treatments:
A. we should use separate t tests because there is a smaller likelihood of computational error.
B. we should use ANOVA to reduce the possibility of a type II error.
C. we should use ANOVA to reduce the possibility of a type I error.
D. None of the above
Question 4 of 40
Three different fertilizers were applied to a field in 7 controlled applications. In computing F, how
many degrees of freedom should there be in the numerator?
A. 1
B. 2
C. 6
D. 12
Question 5 of 40
Answer questions 5-8 using the following information:
Test the hypothesis that the treatment means for samples given below are equal. Use the .01
significance level.
Treatment 1 Treatment 2 Treatment 3
22 34 13
20 31 10
21 25 14
18 25 11
19 32
30
What is the decision rule?
A. Reject the null hypothesis if F > 5.42
B. Reject the null hypothesis if F > 6.93
C. Accept the null hypothesis if F > 26.9
D. Reject the null hypothesis if F > 99.4
Question 6 of 40
Based on the information in the chart in #5, calculate the SS total.
A. -4,132.8
B. 755.83
C. 845.33
D. 4,132.8
Question 7 of 40
Based on the information in the chart in #5, calculate the MSE.
A. 7.46
B. 377.92
C. 422.66
D. 2,066.4
Question 8 of 40
Based on the information in the chart in #5, calculate the F statistic.
A. 1.00
B. 7.46
C. 50.67
D. 54.5
Question 9 of 40
SEE
In an experiment in which two of four similar units are each compressed at three different levels
(light, medium, heavy) to determine resilience, what is the number of degrees of freedom
(numerator, denominator)?
A. (2,3)
B. (2,6)
C. (1,4)
D. (1,3)
Question 10 of 40
Please use the following information to answer questions 10 and 11:
The following data apply to a two-factor ANOVA:
Source 1 2 3
A 12 14 8
B 9 11 9
C788
Calculate the SST for the data.
A. 1.36
B. 10.89
C. 31.11
D. 42.22
Question 11 of 40
Based on the information in the chart in #10, calculate the SSB for the data.
A. 20.22
B. 31.11
C. 53.33
D. 63.11
Question 12 of 40
An F statistic is:
A. a ratio of two means.
B. a ratio of two variances.
C. the difference between three means.
D. a population parameter.
Question 13 of 40
An electronics company wants to compare the quality of their cell phones to the cell phones from
three competitors. They sample 10 phones from each company and count the number of defects
for each phone. If ANOVA is used to compare the average number of defects, the treatments
would be defined as:
A. the number of cell phones sampled.
B. the average number of defects.
C. the total number of phones.
D. the four companies.
Question 14 of 40
Analysis of variance is used to:
A. compare nominal data.
B. compute t test.
C. compare population proportion.
D. simultaneously compare several population means.
Question 15 of 40
When comparing the mean salaries to test for differences between treatment means, the t
statistic based on:
A. the treatment degrees of freedom.
B. the total degrees of freedom.
C. the error degrees of freedom.
D. the ratio of treatment and error degrees of freedom.
Question 16 of 40
When comparing the mean annual incomes for executives with undergraduate degrees and
executives with Master's degrees or more, the following 95% confidence interval can be
constructed as:
A. 2.0 ± 2.052*6.51.
B. 2.0 ± 3.182*6.51.
C. 2.0 ± 2.052*42.46.
D. None of the above
Question 17 of 40
Based on the comparison between the mean annual incomes for executives with undergraduate
and master's degrees or more:
A. a confidence interval shows that the mean annual incomes are not significantly different.
B. the ANOVA results show that the mean annual incomes are significantly different.
C. a confidence interval shows that the mean annual incomes are significantly different.
D. the ANOVA results show that the mean annual incomes are not significantly different.
Question 18 of 40
In a two-way ANOVA, a blocking variable is used to:
A. increase the error sum of squares.
B. decrease the error sum of squares.
C. increase the treatment sum of squares.
D. decrease the treatment sum of squares.
Question 19 of 40
A large department store examined a sample of the 18 credit card sales and recorded the
amounts charged for each of three types of credit cards: MasterCard, Visa, and Discover. Six
MasterCard sales, seven Visa, and five Discover sales were recorded. The store used ANOVA to
test if the mean sales for each credit card were equal. What are the degrees of freedom for the F
statistic?
A. 18 in the numerator, 3 in the denominator
B. 3 in the numerator, 18 in the denominator
C. 2 in the numerator, 15 in the denominator
D. 0 in the numerator, 15 in the denominator
Question 20 of 40
In ANOVA analysis, when the null hypothesis is rejected, we can find which means are different
by:
A. constructing confidence intervals.
B. adding another treatment.
C. doing an additional ANOVA.
D. doing a t test.
Question 21 of 40
The regression equation:
A. can be adjusted to accommodate any number of independent variables.
B. indicates an inverse relationship between variables when a "b" coefficient has a negative sign.
C. should only be used to predict values for the dependent variable that are inside the range of
the sample values.
D. All of the above
Question 22 of 40
The measure of explained variation is the:
A. coefficient of multiple determination.
B. coefficient of multiple nondetermination.
C. regression coefficient.
D. correlation matrix.
Question 23 of 40
An analyst determines the relationship between the time taken to perform a computer-triggered
production function (Y), required memory to run the function (000 bytes), and amount of input
(000 lines of data). The regression equation representing this relationship is determined to
be:Y'=11.43 + 1.26X1 + 3.11X2. For required memory of 25,000 bytes of data, and input of
8,000 lines of data, the estimated time to run the function is:
A. 14.233 minutes.
B. 67.81 minutes.
C. 73.69 minutes.
D. 129.43 minutes.
Question 24 of 40
For a run that required a memory of 15,000 bytes and input of 8,000 lines the time of the run is
54 minutes; this is:
A. 13 minutes less than expected.
B. 1.2 minutes less than expected.
C. 1.2 minutes more than expected.
D. not calculable without additional data.
Question 25 of 40
Please answer questions 5 and 6 using the following information:
A regression analysis yielded the following output:
Constant 23.00371
Std Error of Y estimate 2.91933
R2 0.91404
No. of Observations 21
Degrees of Freedom 15
ABCDE
X coefficients -0.031 0.381 1.452 -0.089 3.554
Std Err of Coef. 0.183 0.158 0.387 0.541 0.833
The multiple regression equation is:
A. Y'=-0.31A +0.381B + 1.452C - 0.089D + 3.554E
B. Y'=23.004 - 0.31A + 0.381B + 1.452C - 0.089D + 3.554E
C. Y'=-23.004 + 0.31A - 0.381B - 1.452C + 0.089D - 3.554E
D. Y'=23.004 - 0.183A +0.158B + 0.387C - 0.541D + 0.833E
Question 26 of 40
The variable with the greatest impact on Y is:
A. B.
B. A.
C. E.
D. D.
Question 27 of 40
The total of the square of each residual is the basis for the calculation of:
A. homoscedasticity.
B. the multiple coefficient of correlation.
C. the multiple standard error of the estimate.
D. multicollinearity.
Question 28 of 40
When the independent variables of a regression are highly correlated the results will exhibit:
A. homoscedasticity.
B. multiple correlation.
C. autocorrelation.
D. multicollinearity.
Question 29 of 40
The __________ test investigates whether all the independent variables have a zero net
regression coefficient.
A. multicollinearity
B. autocorrelation
C. global
D. Pearson
Question 30 of 40
In a regression analysis, three independent variables are used in the equation based on a
sample of forty observations. What are the degrees of freedom associated with the F-statistic?
A. 3 and 39
B. 4 and 40
C. 3 and 36
D. 2 and 39
Question 31 of 40
For a unit change in the first independent variable with other things being held constant, what
change can be expected in the dependent variable in the multiple regression equation Y' = 5.2 +
6.3X1 - 7.1X2?
A. -7.1
B. +6.3
C. +5.2
D. +4.4
Question 32 of 40
In multiple regression analysis, residuals (Y - Y') are used to:
A. provide a global test of a multiple regression model.
B. evaluate multicollinearity.
C. evaluate homoscedasticity.
D. compare two regression coefficients.
Question 33 of 40
What are the degrees of freedom associated with the regression sum of squares?
A. Number of independent variables
B. 1
C. F-ratio
D. (n - 2)
Question 34 of 40
Which test statistic do we apply to test the null hypothesis that the multiple regression
coefficients are all zero?
A. z
B. t
C. F
D. SPSS-X
Question 35 of 40
What does the correlation matrix for a multiple regression analysis contain?
A. Multiple correlation coefficients
B. Simple correlation coefficients
C. Multiple coefficients of determination
D. Multiple standard errors of estimate
Question 36 of 40
A frequent use of a correlation matrix is to check for:
A. coefficients of determination.
B. standard errors of estimate.
C. multicollinearity.
D. confidence intervals.
Question 37 of 40
A manager at a local bank analyzed the relationship between monthly salary and three
independent variables: length of service (measured in months), gender ( 0 = female, 1 = male),
and job type (0 = clerical, 1 = technical). The following ANOVA summarizes the regression
results:
ANOVA
df SS MS F
Regression 3
1004346.771
334782.257
Residual
26
1461134.596
56197.48445
Total
29
2465481.367
5.96
Coefficents Standard Error t Stat P-value
Intercept 784.92 322.25 2.44 0.02
Service 9.19 3.20 2.87 0.01
Gender 222.78 89.00 2.50 0.02
Job -28.21 89.61 -0.31 0.76
Based on the ANOVA and a 0.05 significance level, the global null hypothesis test of the multiple
regression model:
A. will be rejected; conclude that monthly salary is related to all of the independent variables.
B. will be rejected; conclude that monthly salary is related to at least one of the independent
variables.
C. will not be rejected.
D. will show a high multiple coefficient of determination.
Question 38 of 40
Based on the ANOVA table in Question #17, the multiple coefficient of determination is:
A. 5.957%.
B. 59.3%.
C. 40.7%.
D. unable to be computed.
Question 39 of 40
Based on the hypothesis tests for the individual regression coefficients in the ANOVA table in
Question #17:
A. all the regression coefficients are not equal to zero.
B. "job" is the only significant variable in the model.
C. only months of service and gender are significantly related to monthly salary.
D. "service" is the only significant variable in the model.
Question 40 of 40
What can we conclude if the net regression coefficients in the population are not significantly
different from zero?
A. A strong relationship exists among the variables.
B. No relationship exists between the dependent variable and the independent variables.
C. Independent variables are good predictors.
D. Good forecasts are possible.