Self-evaluation test
The following 40 multiple-choice questions give a representative overview what the actual Admission test will be like.
Basic mathematics
What is logk(10k)?
- k*logk(10)
- 10
- k/10
- k*log10(k)
What is (100k)1/2?
What is k-1/2 (for k > 0)?
log(m+n) = log(m) * log(n). Is this statement true or false (for both m and n > 0)?
Below you find the matrices M1 and M2. What is their matrix product, i.e. what is M1T * M2?
Which vector is orthogonal to v (i.e. forms a 90 degree angle with it)?
What is the derivative of f(x) = log(x1/2 + 2) (with respect to x)?
- x1/2 / (2x1/2 + 4)
- -1 / (2x + 4x1/2)
- -x1/2 / (2x1/2 + 4)
- 1 / (2x + 4x1/2)
What is the integral of f(x) = xe2x (with respect to x)?
- (2x - 1)ex / 2 + Constant
- (2x - 1)e2x / 2 + Constant
- (2x - 1)ex / 4 + Constant
- (2x - 1)e2x / 4 + Constant
At what value does the function f(x) = -4x2 + 16x reach a maximum?
- -8
- 0
- 2
- None of the other options: the function f(x) reaches a minimum.
What is the area under the curve f(x) = 6x2 between the values x=-2 and x=2?
Probability
If two fair dice are thrown at the same time, then what is the probability that a 1 is thrown first and a 2 next?
A letter is chosen at random from the word PROBABILITY. What is the probability that it is the letter B or I?
If a family has three children, then what is the probability that the family has AT LEAST two boys? Assume that a child of either gender is equally likely.
If three fair coins are thrown at the same time, then what is the probability of not obtaining three tails?
A company with 60 % male employees has 30 % female employees who work part-time. What is the probability that an employee of the company works part-time given it is a female employee?
If a family has two children, then what is the probability that both of them are girls given that AT LEAST one of them is a girl? Assume that a child of either gender is equally likely.
If a card is randomly drawn from a standard pack of 52 playing cards, then what is the probability of getting a diamond or an ace?
If two fair six-sided dice are thrown at the same time, what is the probability that the sum of the faces showing up is 7?
One bag of 200 marbles has 20% red marbles, 50% blue marbles and 30% green marbles. Another bag of 100 marbles has 20% red marbles, 10% blue marbles and 70% green marbles. Both bags are mixed and a blue marble is randomly drawn from the mix. What is the probability that it came from the first bag?
Given the following probabilities (in percentages) for the ordinal variable X, what is the probability of X smaller than or equal to 1?
X |
Percentage |
0 |
1 |
1 |
3 |
2 |
24 |
3 |
34 |
4 |
26 |
5 |
12 |
Statistics
Consider the data values 10, 5, 6, 17, 13, 9, 19, 14, 7, 9. Their sample mean with 10 % of the values trimmed is 11.250.
Consider the following graph. It shows that the variance of the data is about 5.
Consider the following boxplot (of values drawn from a chi-squared distribution with 1 degree of freedom). It shows that the data values are left-skewed, so the mean is probably bigger than the median.
The covariance of two standardized variables is always equal to their (Pearson's) correlation.
A low p-value suggests that the null hypothesis is true.
Suppose researchers set up a study to evaluate a new treatment for allergies. Beforehand they specify that the chance of erroneously missing an effect equals 15%, while the chance of erroneously finding an effect equals 10%. When the eventual analysis returns a p-value of 0.12, the researchers will not reject the null hypothesis.
If you falsely do not reject the null hypothesis in a statistical hypothesis test, then you have a so-called significant result.
Consider a one-sample t-test for H0: μ = 0. For a lower sample average but with the same sample size and sample variance the p-value can be expected to decrease.
Consider the chi-square test for a frequency table. Its null hypothesis implies that the distribution across the columns depends on the rows.
A farmer compares two fertilizing methods by means of a t-test. The 95 % confidence interval of the difference in mean yield between both methods is [-50; 850] euro. This implies that the difference in mean yield in this specific study is 400 euro.
R programming
The function load() loads a package in R and the function help() opens a help page.
- False for load() and false for help()
- False for load() but true for help()
- True for load() but false for help()
- True for load() and true for help()
Consider a vector x with 100 values in R. The command x[x == 50] selects those elements in x which are equal to 50 and the command x[-99] selects the one but last element in x.
- False for x[x == 50] and false for x[-99]
- True for x[x == 50] but false for x[-99]
- False for x[x == 50] but true for x[-99]
- True for x[x == 50] and true for x[-99]
With which R commands do you create the vectors [3, 2, 1,…, 3, 2, 1] and [5, 5, 5,…, 9, 9, 9] (each of length 15)?
- rep(3:1, times = 5) and rep(5:9, each = 3)
- rep(3:1, each = 5) and rep(5:9, times = 3)
Which R command implements the following mathematical expression (considering that the xi values are stored in a vector x of length N)?
- sum((x – sum(x)/len(x))^2) / len(x)
- sum((x – sum(x)/length(x))^2) / length(x)
- summate((x – summate(x)/len(x))^2) / len(x)
- summate((x – summate(x)/length(x))^2) / length(x)
The command for (i in 1:(length(x) - 1)) { x[i] <- x[i] + x[i + 1] } does the same as the function cumsum() and the command while (sum(y) < 10) { y <- y * 2 } will double each element in y (you can assume that x and y are existing objects in R).
- False for the for command and false for the while command
- True for the for command and true for the while command
- False for the for command but true for the while command
- True for the for command but false for the while command
If mat is a 100x100 matrix, and both vec1 and vec2 are vectors of 100 elements, then the commands rbind(cbind(mat, vec1), vec2) and cbind(cbind(mat, vec1), vec2) will produce a 101x101 matrix.
- False for rbind(cbind(mat, vec1), vec2) and false for cbind(cbind(mat, vec1), vec2)
- True for rbind(cbind(mat, vec1), vec2) and true for cbind(cbind(mat, vec1), vec2)
- True for rbind(cbind(mat, vec1), vec2) but false for cbind(cbind(mat, vec1), vec2)
- False for rbind(cbind(mat, vec1), vec2) but true for cbind(cbind(mat, vec1), vec2)
The R function average() computes the statistical average of a vector and the function mode() computes its statistical mode.
- False for average() and false for mode()
- False for average() but true for mode()
- True for average() but false for mode()
- True for average() and true for mode()
Consider a numeric vector y in R and a grouping vector x (both of the same length). You can do a two-sided t-test with the R command t.test(y ~ x) and you can access its p-value with the command t.test(y ~ x)@p.value.
- False for t.test(y ~ x) and false for t.test(y ~ x)@p.value
- False for t.test(y ~ x) but true for t.test(y ~ x)@p.value
- True for t.test(y ~ x) but false for t.test(y ~ x)@p.value
- True for t.test(y ~ x) and true for t.test(y ~ x)@p.value
The function tr() generates t-distributed random values in R and the function fd() gives the probability under an F-distribution.
- False for tr() and false for fd()
- False for tr() but true for fd()
- True for tr() but false for fd()
- True for tr() and true for fd()
Which function in R is a high-level plotting function (i.e. it creates a new plot) and which is a low-level plotting function (i.e. it adds information to an existing plot)?
- High-level: text(), low-level: title()
- High-level: hist(), low-level: title()
- High-level: hist(), low-level: barplot()
- High-level: barplot(), low-level: hist()
Scores
Since the Admission test consists of multiple-choice questions, it is marked according to
Ghent University's regulations on multiple-choice tests. In addition, you need to correctly answer at least half of the questions in each of the four subsections (i.e.
Basic mathematics,
Probability,
Statistics and
R programming). Finally, you need to complete the test within 70 minutes.
The correct answers to the questions above are:
- k*logk(10)
- 10k
- 1/k0.5
- False
- MC
- vC
- 1 / (2x + 4x1/2)
- (2x - 1)e2x / 4 + Constant
- 2
- 32
- 1/36
- 4/11
- 1/2
- 7/8
- 3/4
- 1/3
- 4/13
- 1/6
- 10/11
- 1/25
- False
- False
- False
- True
- False
- True
- False
- False
- False
- True
- False for load() but true for help()
- True for x[x == 50] but false for x[-99]
- rep(3:1, times = 5) and rep(5:9, each = 3)
- sum((x – sum(x)/length(x))^2) / length(x)
- False for the for command and false for the while command
- False for rbind(cbind(mat, vec1), vec2) and false for cbind(cbind(mat, vec1), vec2)
- False for average() and false for mode()
- True for t.test(y ~ x) but false for t.test(y ~ x)@p.value
- False for tr() and false for fd()
- High-level: hist(), low-level: title()