Master of science in Statistical Data-analysis

  1. Study guide
  2. Master of science in statistical data-analysis
  3. Admission
  4. Assessment test
  5. Self-evaluation test

Self-evaluation test

The following 30 multiple-choice questions give a representative overview of the 40 multiple-choice questions of the actual Admission test.

Basic mathematics

What is logk(10k)?

  • k*logk(10)
  • 10
  • k/10
  • k*log10(k)

What is (100k)1/2?

  • 1/10k
  • 10k
  • 50k
  • k50

What is k-1/2 (for k >= 0)?

  • 1/k0.5
  • -k0.5
  • k2
  • 21/k

em+n = em + en. Is this statement true or false?

  • True
  • False

log(m+n) = log(m) * log(n). Is this statement true or false (for both m and n > 0)?

  • True
  • False

log(1/m) = -log(m). Is this statement true or false (for m > 0)?

  • True
  • False

Below you find the matrices M1 and M2. What is their matrix product, i.e. what is M1T * M2?



  • MA
  • MB
  • MC
  • MD

Which vector is orthogonal to v (i.e. forms a 90 degree angle with it)?



  • vA
  • vB
  • vC
  • vD

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?

  • 0
  • 16
  • 32
  • 48

Probability

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.

  • 3/8
  • 1/3
  • 1/2
  • 2/3

If two fair dice are thrown at the same time, what is the probability that you get a 1 is thrown first and a 2 next?

  • 1/36
  • 1/18
  • 1/6
  • 1/3

A letter is chosen at random from the word PROBABILITY. What is the probability that it is the letter B or I?

  • 4/11
  • 2/11
  • 1/4
  • 1/2

If three fair coins are thrown at the same time, then what is the probability of not obtaining three tails?

  • 1/3
  • 2/3
  • 7/8
  • 8/8

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?

  • 3/4
  • 12/100
  • 3/10
  • 4/10

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.

  • True
  • False

Consider the following graph. It shows that the variance of the data is about 5.



  • True
  • False

A low p-value suggests that the null hypothesis is true.

  • True
  • False

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.

  • True
  • False

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.

  • True
  • False

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 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
  • False
  • True
  • MC
  • vC
  • 1 / (2x + 4x1/2)
  • (2x - 1)e2x / 4 + Constant
  • 2
  • 32
  • 1/2
  • 1/36
  • 4/11
  • 7/8
  • 3/4
  • False
  • False
  • False
  • True
  • 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 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()