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# Multiple Choice questions testing of Hypothesis

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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.

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.

Three different fertilizers were applied to a field in 7 controlled applications. In computing F, there should be _______degrees of freedom in the numerator:

a. 1
b. 2
c. 6
d. 12

Answer questions the next four questions 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

The decision rule is:

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

SS total is:

a. -4,132.8
b. 755.83
c. 845.33
d. 4,132.8

MSE is:
a. 7.46
b. 377.92
c. 422.66
d. 2,066.4

The F statistic =
a. 1.00
b. 7.46
c. 50.67
d. 54.5

In an experiment in which two of four similar units are each compressed at three different levels (light, medium, heavy) to determine resilience, the number of degrees of freedom (numerator, denominator) is:

a. (2,3)
b. (2,6)
c. (1,4)
d. (1,3)

The following data apply to a two-factor ANOVA:

Treatment
Source 1 2 3
A 12 14 8
B 9 11 9
C 7 8 8

SST for the data =
a. 1.36
b. 10.89
c. 31.11
d. 42.22

SSB for the data =
a. 20.22
b. 31.11
c. 53.33
d. 63.11

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. Both a and b.
e. All of the above

The measure of explained variation is the:
a. coefficient of multiple determination.
b. Coefficient of multiple non-determination.
c. Regression coefficient.
d. Correlation matrix

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:

Y1 = 11.43 + 1.26X 1 + 3.11X 2
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
e. Not calculable without additional data.

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.

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

A B C D E
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. Y1 = -0.31A + 0.381B + 1.452C - 0.089D + 3.554E
b. Y1 = 23.004 - 0.31A + 0.381B + 1.452C - 0.089D + 3.554E
c. Y1 = -23.004 + 0.31A - 0.381B - 1.452C + 0.089D - 3.554E
d. Y1 = 23.004 - 0.183A + 0.158B + 0.387C - 0.541D + 0.833E

The variable with the greatest impact on Y is:
a. A
b. B
c. C
d. D
e. E

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

When the independent variables of a regression are highly correlated the results will exhibit:
a. homoscedasticity
b. multiple correlation
c. autocorrelation
d. multicollinearity

The test investigates whether all of the independent variable have a zero net regression coefficient.
a. multicollinearity
b. autocorrelation
c. global
d. Pearson

Answer the next five question based on the following information:
For a sample size of 15 observations, the regression equation presented in question #14 resulted in total variation is 1,985.7332, and unexplained variation is 158.7286.

The multiple standard error of the estimate is:

a. 1.05
b. 3.49
c. 3.64
d. 3.80

The mean square of the regression is
a. 13.23
b. 79.36
c. 152.25
d. 913.5
e. 992.87

At a significance level of a = .01, the computed value of F indicates that:

a. the independent variables are useful in predicting the value of the dependent variable.
b. The independent variables are not useful in predicting the value of the dependent variable

Based on the analysis of variance we would fail to reject H0.
a. True
b. False

Using a significance level of 0.05, the null hypothesis for both the treatments and the blocks will be rejected.
a. True
b. False