dmuwodmfdmuwodmfdmuwodmf-2dbccd83e4b5901d99a312b69c417190
Question 1
Suppose you roll two dice. The statement ‘The sum of the two numbers is odd’ corresponds
to:
a) A quantitative random variable
b) An elementary outcome and an event
c) An event but not an elementary outcome
You could roll 1 and 2 which gives 3, so (1 ; 2) is an elementary outcome.
But you could also roll 1 and 4 which gives 5, so (1 ; 4) is an elementary outcome.
But since multiple results can give something where “the sum of the two numbers is odd”, we have
an event.
Question 2
Suppose that if you randomly draw a single person from a population, then P(neurotic) =
0.10. Likewise, P(color blind) = 0.06. Furthermore, it turns out that P(neurotic AND color
blind) = 0.04. This implies that:
a) ‘Neurotic’ and ‘color blind’ are two disjoint events but they are not independent
b) ‘Neurotic’ and ‘color blind’ are not disjoint events and they are not independent
c) ‘Neurotic’ and ‘color blind’ are independent events but it is impossible to tell if they
are also disjoint
If independent P(A and B) = P(A) * P(B). → 0.1*0.06 = 0.006 which isn’t equal to 0.04, so not
independent!
If events are disjoint P(A and B) = P(A|B) = 0 → is not 0.04 so not disjoint!
Question 3
Consider the following population of 1000 persons, in which everyone can be classified
according to age (Young or Old) and Gender (Male or Female):
Suppose that a single person is drawn at random from this population. What is the
probability that the person is a female given that the person is young, that is
P(Female|Young)?
a) 0.50
b) 0.17
c) 0.60
P(A|B) = #A within B / #B → = 0.5
Question 4
Refer back to the population specified in Question 3, but now suppose that a simple random
sample of size n=2 is drawn from this population. Suppose that X is the random variable
'number of males in the sample of size n=2'. What is the probability associated to X=2 (i.e.
two males)?
a) 0.16
b) 0.01
c) 0.50
P(X= 2) = (400/1000) *( 400/ 1000) = 0.16
Question 5
In a population of epileptic patients, the number of seizures per month (X) is distributed as
Find more resources on this topic on
, dmuwodmfdmuwodmfdmuwodmf-2dbccd83e4b5901d99a312b69c417190
indicated by the table below
Suppose that you take a simple random sample of size n=1 from this population. What is the
probability that the patient has less than 7 and more than 4 seizures per month, which is
P(X<7 AND X>4)?
a) 0.30
b) The random variable X is not Normally distributed, thus the requested probability
cannot be determined
c) 0.36
P(5 or 6) = 0.1 + 0.2 = 0.3
Question 6
Suppose that the variable 'body weight in kg' is normally distributed in a certain male
population, with population mean equal to 75 and population standard deviation equal to
12. Suppose a simple random sample of size n=9 is drawn from this male population. What is
the probability that the sample mean is larger than 78?
a) 0.07
b) 0.23
c) This probability cannot be determined using Table A, since the sample size is not
large enough to apply the Central Limit Theorem
z = (~x - µ) / (σ / √N )
→z = (78 – 75 ) / (12 / √9) = 0.75
p-value = 0.23
For C: central limit theorem does not apply, but it was said the population itself is normally
distributed already.
Question 7
Suppose that the variable 'number of seizures' is skewed to the left in a certain population of
epilepsy patients. Also, suppose that you collect a sample of size n=30. Which statement is
certainly correct?
a) The shape of the population distribution is approximately normal
b) The shape of the distribution of the ‘number of seizures’ scores is approximately
normal in the sample
c) The shape of the sampling distribution of the mean number of seizures is
approximately normal
This because the central limit theorem applies (N > 25)
Question 8
A researcher is interested in the mean IQ score of the Belgian population. He will draw a
simple random sample from the Belgian population and he will use the mean IQ score in the
sample as a statistic for the mean IQ score of the Belgian population. Consider the following
two options: Option A implies that he will draw a simple random sample of size n=10; Option
B implies that he will draw a simple random sample of size n=100. Which statement is
correct?
a) In both options the statistic is an unbiased statistic for the mean IQ score of the
Belgian population
b) In none of the two options the statistic is an unbiased statistic for the mean IQ score
Save time with the right summary on
Question 1
Suppose you roll two dice. The statement ‘The sum of the two numbers is odd’ corresponds
to:
a) A quantitative random variable
b) An elementary outcome and an event
c) An event but not an elementary outcome
You could roll 1 and 2 which gives 3, so (1 ; 2) is an elementary outcome.
But you could also roll 1 and 4 which gives 5, so (1 ; 4) is an elementary outcome.
But since multiple results can give something where “the sum of the two numbers is odd”, we have
an event.
Question 2
Suppose that if you randomly draw a single person from a population, then P(neurotic) =
0.10. Likewise, P(color blind) = 0.06. Furthermore, it turns out that P(neurotic AND color
blind) = 0.04. This implies that:
a) ‘Neurotic’ and ‘color blind’ are two disjoint events but they are not independent
b) ‘Neurotic’ and ‘color blind’ are not disjoint events and they are not independent
c) ‘Neurotic’ and ‘color blind’ are independent events but it is impossible to tell if they
are also disjoint
If independent P(A and B) = P(A) * P(B). → 0.1*0.06 = 0.006 which isn’t equal to 0.04, so not
independent!
If events are disjoint P(A and B) = P(A|B) = 0 → is not 0.04 so not disjoint!
Question 3
Consider the following population of 1000 persons, in which everyone can be classified
according to age (Young or Old) and Gender (Male or Female):
Suppose that a single person is drawn at random from this population. What is the
probability that the person is a female given that the person is young, that is
P(Female|Young)?
a) 0.50
b) 0.17
c) 0.60
P(A|B) = #A within B / #B → = 0.5
Question 4
Refer back to the population specified in Question 3, but now suppose that a simple random
sample of size n=2 is drawn from this population. Suppose that X is the random variable
'number of males in the sample of size n=2'. What is the probability associated to X=2 (i.e.
two males)?
a) 0.16
b) 0.01
c) 0.50
P(X= 2) = (400/1000) *( 400/ 1000) = 0.16
Question 5
In a population of epileptic patients, the number of seizures per month (X) is distributed as
Find more resources on this topic on
, dmuwodmfdmuwodmfdmuwodmf-2dbccd83e4b5901d99a312b69c417190
indicated by the table below
Suppose that you take a simple random sample of size n=1 from this population. What is the
probability that the patient has less than 7 and more than 4 seizures per month, which is
P(X<7 AND X>4)?
a) 0.30
b) The random variable X is not Normally distributed, thus the requested probability
cannot be determined
c) 0.36
P(5 or 6) = 0.1 + 0.2 = 0.3
Question 6
Suppose that the variable 'body weight in kg' is normally distributed in a certain male
population, with population mean equal to 75 and population standard deviation equal to
12. Suppose a simple random sample of size n=9 is drawn from this male population. What is
the probability that the sample mean is larger than 78?
a) 0.07
b) 0.23
c) This probability cannot be determined using Table A, since the sample size is not
large enough to apply the Central Limit Theorem
z = (~x - µ) / (σ / √N )
→z = (78 – 75 ) / (12 / √9) = 0.75
p-value = 0.23
For C: central limit theorem does not apply, but it was said the population itself is normally
distributed already.
Question 7
Suppose that the variable 'number of seizures' is skewed to the left in a certain population of
epilepsy patients. Also, suppose that you collect a sample of size n=30. Which statement is
certainly correct?
a) The shape of the population distribution is approximately normal
b) The shape of the distribution of the ‘number of seizures’ scores is approximately
normal in the sample
c) The shape of the sampling distribution of the mean number of seizures is
approximately normal
This because the central limit theorem applies (N > 25)
Question 8
A researcher is interested in the mean IQ score of the Belgian population. He will draw a
simple random sample from the Belgian population and he will use the mean IQ score in the
sample as a statistic for the mean IQ score of the Belgian population. Consider the following
two options: Option A implies that he will draw a simple random sample of size n=10; Option
B implies that he will draw a simple random sample of size n=100. Which statement is
correct?
a) In both options the statistic is an unbiased statistic for the mean IQ score of the
Belgian population
b) In none of the two options the statistic is an unbiased statistic for the mean IQ score
Save time with the right summary on
