Practice Exam 2016/2017: Statistics II for IB - UG

Questions

Question 1

Which of the following statments is TRUE?

1. Both a bar chart and a box&whiskers plot can be used to represent qualitative data.
2. Scatter plots can be used to represent qualitative and quantitative data both:
3. Quantitative data. can be represented on histograms or on a box&whiskers plot.
4. On a box&whiskefs plot the box contains the proportion of those observations which are within one standard deviation of the mean.

Question 2

Which of the following statments is TRUE? The statistical power of a. test increases if (ceteris paribus)..

1. the effect size decreases, the probability of type I error decreases or the sample size decreases
2. the effect size increases, the probability of type I error increases or the sample size increases
3. the effect size increases, the probability of type I error decreases or the sample size increases
4. the effect size decreases, the probability of type I error increases or the sample size decreases

Question 3

Let α denote the probability of making a type I error and ß the probability of making a type II error. Which of the following statments is TRUE?

1. The statistical power of a test equals to 1 — α.
2. The probability of rejecting a true nuflhypothesis equals 1 — ß.
3. The probability of rejecting a false nullhypothesis 15 also known as the statistical power of the test.
4. The probability of not rejecting a false nullhypothesis equals to α.

Question 4

We calculated the Mahalanobis distance of all 28 metric variables and found that the largest value belongs to Oman With 2.20. What conclusions can be drawn?

1. Based on the Mahalanobis distance measure no observations need to be removed from the dataset.
2. Based on the Mahalanobis distance measure Oman should be removed from the dataset, and there might be other observations which should be removed.
3. Based on the Mahalanobis distance measure Oman should not be removed from the dataset, but there could be extremely low values of the Mahalanobis distance measure which would justify removing other observations.
4. No conclusion can be drawn because the sample size (n = 196)'is not big enough.

Question 5

Which test statistic is used to test for the heterosketasticity of the variance of a variable?

1. Pearson
2. Levene
3. t—test
4. Shapiro-Wifli

Question 6

Which of the followirig is the least critical statistical assumption of the multivariate regression analysis (MBA)?

1. Multicollinearity
2. Linearity
3. Homoskedasticity
4. Independence of errors

Question 7

What is the minimum number of observations per variabie so that the MBA is allowed?

1. 5
2. 10
3. 15
4. 100

Question 8

What is the goal of Ordinary Least Squares?

1. To minimize the sum of squared parameter estimates.
2. To estimate the coefficients of a statistical model With the smallest possible errors.
3. To minimize the average of the residuals.
4. None of the above.

Question 9

Which of the following statements is TRUE?

1. The higher the tolerance of a variable is the higher its Variance Inflating Factor will be.
2. The VIF value of a variable is independent of its tolerance value.
3. The tolerance value of a variable equals tothe R² value of such a regression model where the chosen variable is the predicted variable and all other independent variables are used as predictors.
4. The tolerance value of a variable equals to 1 — R² of such a regression model where the chosen variable is the predicted variable and all other independent variables are used as predictors.

Question 10

Which of the fellowing statrnents is TRUE?

1. The primary purpose of factor analysis is to analyze the relationships between variables in the analysis.
2. The primary purpose of factor analysis is to analyze the relationships between one categorical dependent variable and several metric independent variables.
3. The primary purpose of factor analysis is to define the underlying structure among the variables in the analysis.
4. The primary purpose of factor analysis is to analyze the variability of variables in the analysis.

Question 11

Which of the following statments is TRUE?

1. Exploratory factory analysis is useful when we want to test a measurement theory on the number of factors that best represent the data.
2. Confirmatory factory analysis is useful When we want to know the structure (of patterns) that best represent the data.
3. Exploratory factory analysis is useful when we want to test the structure (or patterns) that best represent the data.
4. Confirmatory factory analysis is useful when we want to test the structure (or patterns) and the number of factors that best represent the data.

Question 12

Which method provided below suffers from factor indeterminanoy? Factor indeterminanoy means that for any individual respondent, several difierent factor scores can be calculated from a single-faotor model result.

1. Common Factor Analysis.
2. Principal Component Analysis.
3. Multivariate Regression Analysis.
4. Factor Variance Analysis.

Question 13

For Factor Analysis, the presence of correlated variables and the subsequent definition of factors do not guarantee relevance, even if they meet the statistical requirements. This is equivalent to say that:

1. For Factor Analysis, the statistical asSumptions are more critical than conceptual assumptions.
2. For Factor Analysis, the conceptual assumptions are more critical than statistical assumptions.
3. For Factor Analysis, there are no critical assumptions at all.
4. For Factor Analysis, conceptual and statistical assumptions are equally critical.

Question 14

In Factor Analysis, rotation methods can be used to:

1. Extract the optimal number of factors in factor solutions.
2. Increase the variance explained by the factor solutions.
3. Provide a better interpretation of the factor solutions.
4. Increase the statistical significance of factor solutions.

Question 15

Which of the following statements is TRUE?

1. Orthogonal rotational techniques are used for the objective of data reduction.
2. Orthogonal rotational techniques allow correlated factors.
3. Oblique rotational techniques maintain the independendce between factors.
4. Oblique rotations are similar to orthogonal rotations, except that oblique rotations allow correlated factors.

Question 16

In factor analysis, the explained variance extracted by the factor solution is similar with:

1. Percentage of trace.
2. Factor loadings.
3. Identity matrix.
4. Scree test.

Question 17

A researcher intends to use Factor Analysis on a dataset which includes 10 metric and 2 nonmetrio variables, and 100 observations. Which of the following statements is TRUE?

1. Because Factor Analysis is not allowed to be applied, the researcher should find another analysis method.
2. Because the sample size is too small the researcher should collect more observations.
3. Because non metric variables are problematic for Factor Analysis, the researcher should recode the non metric variablesinto dummy variables.
4. As there are no problems with this dataset, the researcher can apply Factor Analysis right away.

Answers

Question 1

C

Question 2

B

Question 3

C

Question 4

A

Question 5

B

Question 6

C

Question 7

B

Question 8

B

Question 9

D

Question 10

C

Question 11

D

Question 12

A

Question 13

B

Question 14

C

Question 15

D

Question 16

A

Question 17

C