PYC3704
EXAM PACK
2023
QUESTIONS
AND
ANSWERS
,1. 1 Answer: The correct option is 1
Reasoning:
• Alternative 1 is correct because a theory is defined as a “network of postulated
relations between constructs”.
• Alternative 2 is wrong because one does not test relations between
hypotheses, but between variables.
• The relations are postulated (and therefore not verified) so that alternative 3 is
also incorrect.
2. 3 Answer: The correct option is 3
Reasoning:
The dependent variable is dependent on the independent variable, or conversely,
the independent variable influences the dependent variable. X affects Y (X is the
independent variable and Y is the dependent variable)
3. 3 Answer: The correct option is 3
Reasoning:
A hypothesis is an educated guess, while a theory is a postulated relation between
a set of constructs.
4. 2 Answer: The correct option is 2
Reasoning:
Operational definitions are used to cross the gap between theory and empirical
research. It does this by describing theoretical constructs in terms of observable
instances, which can be measured and used to test a theory.
5. 1 Answer: The correct option is 1
6. 2 Answer: The correct option is 2
Reasoning:
Intelligence is a latent variable because it cannot be observed directly. The results
of the psychometric test can however be observed directly and can therefore be
regarded as the manifest variable.
7. 2 Answer: The correct option is 2
Reasoning:
• Alternative 2 is correct, because a specific hypothesis is now derived from the
theory presented in the scenario.
• Alternatives 1 and 3 is incorrect because the terms ‘estimated size’ and ‘haziness’
have not been operationally defined in the statement given.
8. 3 Answer: The correct option is 3
Reasoning:
(The dependent variable is usually the one that the researcher is interested in, the
variable that is the focus of the research. The independent variable is something
that the researcher manipulates, to see how this affects the dependent variable (in
other words, the dependent variable is dependent on the independent variable).)
9. 1 Answer: The correct option is 1
10. 3 Answer: The correct option is 3
11. 3 Answer: The correct option is 3
12. 2 Answer: The correct option is 2
, Reasoning:
The independent variable is something that the researcher manipulates, to see
how this affects the dependent variable (in other words, the dependent variable is
dependent on the independent variable).
13. 3 Answer: The correct option is 3
14. 1 Answer: The correct option is 1
Reasoning: p(G) = 12/47 = 0.255
15. 2 Answer: The correct option is 2
16. 3 Answer: The correct option is 3
17. 2 Answer: The correct option is 2
18. 1 Answer: The correct option is 1
Reasoning:
z=
80−60
10
=
20
10
=2
19. 1 Answer: The correct option is 1
20. 3 Answer: The correct option is 3
Reasoning:
Z=
35−23
8
= 1.5.
Looking the value 1.5 up in the probabilities associated with standard normal
distribution, under the “greater than” column (since the question states ‘more
than’), the answer is 0.9332.
21. 3 Answer: The correct option is 3
Reasoning:
Σ(𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑐𝑜𝑢𝑛𝑡 𝑜𝑓 𝑐𝑜𝑟𝑟𝑒𝑐𝑡 𝑟𝑒𝑠𝑝𝑜𝑛𝑠𝑒𝑠 7 𝑡𝑜 10)
Σ𝑡𝑜𝑡𝑎𝑙 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑐𝑜𝑢𝑛𝑡
= 17+9+6
1+4+11+14+18+22+17+9+6
= 32
102
= 0.32
22. 1 Answer: The correct option is 1
Where σ denotes the standard deviation, and n denotes the sample size.
23. 1 Answer: The correct option is 1
Reasoning:
CONDITIONAL PROBABILITY - a particular probability is conditional on something
else happening. Event A conditional on Event B happening = P (A B)
24. 1 Answer: The correct option is 1
Reasoning:
The formula p (50% pass) should be read as the conditional probability of someone
obtaining 50%. It is clear from the example that any student selected from the
given population who obtained 50% or more, has necessarily also passed.
, 25. 3 Answer: The correct option is 3
Reasoning:
It often happens that we doubt the assumption that the population distribution is
normal. However, the central limit theorem states that, for a large sample size, the
sampling distribution of a mean is close to normal, irrespective of the shape of the
population distribution of the original data. This enables us to make inferences
about means and develop test statistics for means.
26. 2 Answer: The correct option is 2
27. 1 Answer: The correct option is 1
Reasoning:
If a large effect does not yield a significant result, it may be that the statistical test
lacks power (see section 3.3.2) and increasing the sample size will increase the
power of the test (i.e. its ability to detect significant differences).
28. 3 Answer: The correct option is 3
Reasoning:
We know that a z-scores of -3 (look in the z-tables) are extremely unlikely. We also
know that the negative sign indicates that H1 has a logical chance of being correct
instead of H0 (the result is in the correct direction). This result of -3 is highly
unlikely under H0 and H0 should be rejected in favour of H1. This all means that we
need not find the p-value because we know it will be very small.
29. 3 Answer: The correct option is 3
Reasoning:
A major determinant of the sensitivity or power of a statistical test is sample size
(which is why we can increase sample size to enhance power). When the sample is
large, even smaller effects will have statistical significance. One way that
statisticians have suggested to deal with this problem is by the notion of effect
size.
30. 2 Answer: The correct option is 2
Reasoning:
The researcher compares the p-value with a level of significance (a) that he/she
chose before he/she did the sampling and made the observation. This is chosen by
the researcher, based on the risk of being wrong when rejecting the null
hypothesis that he or she is willing to take.
31. 1 Answer: The correct option is 1
Reasoning:
The Type II error of failing to reject a null hypothesis that is really false is indicated
by the Greek symbol β which indicates the probability associated with this risk.
32. 3 Answer: The correct option is 3
Reasoning:
The null hypothesis is never accepted. The decision regarding the null hypothesis is
to reject it or not to reject it. Therefore alternative 2 is eliminated. If the p-value is
equal to or less than the chosen significance level α, we reject H0 in favour of H1.
Otherwise, do not reject the null hypothesis in favour of the alternative
hypothesis.
33. 2 Answer: The correct option is 2
Reasoning:
Alternative 3 is the null hypothesis.
34. 3 Answer: The correct option is 3
35. 2 Answer: The correct option is 2
Reasoning:
One-tailed = directional.
Two-tailed = non-directional.
Since the hypothesis is H1: μ < 100, this requires a directional and therefore one-
tailed test.
36. 3 Answer: The correct option is 3
37. 1 Answer: The correct option is 1
38. 2 Answer: The correct option is 2
EXAM PACK
2023
QUESTIONS
AND
ANSWERS
,1. 1 Answer: The correct option is 1
Reasoning:
• Alternative 1 is correct because a theory is defined as a “network of postulated
relations between constructs”.
• Alternative 2 is wrong because one does not test relations between
hypotheses, but between variables.
• The relations are postulated (and therefore not verified) so that alternative 3 is
also incorrect.
2. 3 Answer: The correct option is 3
Reasoning:
The dependent variable is dependent on the independent variable, or conversely,
the independent variable influences the dependent variable. X affects Y (X is the
independent variable and Y is the dependent variable)
3. 3 Answer: The correct option is 3
Reasoning:
A hypothesis is an educated guess, while a theory is a postulated relation between
a set of constructs.
4. 2 Answer: The correct option is 2
Reasoning:
Operational definitions are used to cross the gap between theory and empirical
research. It does this by describing theoretical constructs in terms of observable
instances, which can be measured and used to test a theory.
5. 1 Answer: The correct option is 1
6. 2 Answer: The correct option is 2
Reasoning:
Intelligence is a latent variable because it cannot be observed directly. The results
of the psychometric test can however be observed directly and can therefore be
regarded as the manifest variable.
7. 2 Answer: The correct option is 2
Reasoning:
• Alternative 2 is correct, because a specific hypothesis is now derived from the
theory presented in the scenario.
• Alternatives 1 and 3 is incorrect because the terms ‘estimated size’ and ‘haziness’
have not been operationally defined in the statement given.
8. 3 Answer: The correct option is 3
Reasoning:
(The dependent variable is usually the one that the researcher is interested in, the
variable that is the focus of the research. The independent variable is something
that the researcher manipulates, to see how this affects the dependent variable (in
other words, the dependent variable is dependent on the independent variable).)
9. 1 Answer: The correct option is 1
10. 3 Answer: The correct option is 3
11. 3 Answer: The correct option is 3
12. 2 Answer: The correct option is 2
, Reasoning:
The independent variable is something that the researcher manipulates, to see
how this affects the dependent variable (in other words, the dependent variable is
dependent on the independent variable).
13. 3 Answer: The correct option is 3
14. 1 Answer: The correct option is 1
Reasoning: p(G) = 12/47 = 0.255
15. 2 Answer: The correct option is 2
16. 3 Answer: The correct option is 3
17. 2 Answer: The correct option is 2
18. 1 Answer: The correct option is 1
Reasoning:
z=
80−60
10
=
20
10
=2
19. 1 Answer: The correct option is 1
20. 3 Answer: The correct option is 3
Reasoning:
Z=
35−23
8
= 1.5.
Looking the value 1.5 up in the probabilities associated with standard normal
distribution, under the “greater than” column (since the question states ‘more
than’), the answer is 0.9332.
21. 3 Answer: The correct option is 3
Reasoning:
Σ(𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑐𝑜𝑢𝑛𝑡 𝑜𝑓 𝑐𝑜𝑟𝑟𝑒𝑐𝑡 𝑟𝑒𝑠𝑝𝑜𝑛𝑠𝑒𝑠 7 𝑡𝑜 10)
Σ𝑡𝑜𝑡𝑎𝑙 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑐𝑜𝑢𝑛𝑡
= 17+9+6
1+4+11+14+18+22+17+9+6
= 32
102
= 0.32
22. 1 Answer: The correct option is 1
Where σ denotes the standard deviation, and n denotes the sample size.
23. 1 Answer: The correct option is 1
Reasoning:
CONDITIONAL PROBABILITY - a particular probability is conditional on something
else happening. Event A conditional on Event B happening = P (A B)
24. 1 Answer: The correct option is 1
Reasoning:
The formula p (50% pass) should be read as the conditional probability of someone
obtaining 50%. It is clear from the example that any student selected from the
given population who obtained 50% or more, has necessarily also passed.
, 25. 3 Answer: The correct option is 3
Reasoning:
It often happens that we doubt the assumption that the population distribution is
normal. However, the central limit theorem states that, for a large sample size, the
sampling distribution of a mean is close to normal, irrespective of the shape of the
population distribution of the original data. This enables us to make inferences
about means and develop test statistics for means.
26. 2 Answer: The correct option is 2
27. 1 Answer: The correct option is 1
Reasoning:
If a large effect does not yield a significant result, it may be that the statistical test
lacks power (see section 3.3.2) and increasing the sample size will increase the
power of the test (i.e. its ability to detect significant differences).
28. 3 Answer: The correct option is 3
Reasoning:
We know that a z-scores of -3 (look in the z-tables) are extremely unlikely. We also
know that the negative sign indicates that H1 has a logical chance of being correct
instead of H0 (the result is in the correct direction). This result of -3 is highly
unlikely under H0 and H0 should be rejected in favour of H1. This all means that we
need not find the p-value because we know it will be very small.
29. 3 Answer: The correct option is 3
Reasoning:
A major determinant of the sensitivity or power of a statistical test is sample size
(which is why we can increase sample size to enhance power). When the sample is
large, even smaller effects will have statistical significance. One way that
statisticians have suggested to deal with this problem is by the notion of effect
size.
30. 2 Answer: The correct option is 2
Reasoning:
The researcher compares the p-value with a level of significance (a) that he/she
chose before he/she did the sampling and made the observation. This is chosen by
the researcher, based on the risk of being wrong when rejecting the null
hypothesis that he or she is willing to take.
31. 1 Answer: The correct option is 1
Reasoning:
The Type II error of failing to reject a null hypothesis that is really false is indicated
by the Greek symbol β which indicates the probability associated with this risk.
32. 3 Answer: The correct option is 3
Reasoning:
The null hypothesis is never accepted. The decision regarding the null hypothesis is
to reject it or not to reject it. Therefore alternative 2 is eliminated. If the p-value is
equal to or less than the chosen significance level α, we reject H0 in favour of H1.
Otherwise, do not reject the null hypothesis in favour of the alternative
hypothesis.
33. 2 Answer: The correct option is 2
Reasoning:
Alternative 3 is the null hypothesis.
34. 3 Answer: The correct option is 3
35. 2 Answer: The correct option is 2
Reasoning:
One-tailed = directional.
Two-tailed = non-directional.
Since the hypothesis is H1: μ < 100, this requires a directional and therefore one-
tailed test.
36. 3 Answer: The correct option is 3
37. 1 Answer: The correct option is 1
38. 2 Answer: The correct option is 2
