PYC3704 - Psychological Research (2021 - Semester 1 and Semester 2 - Assignment 2 Answers) (With Elaborations)
PYC3704 - Psychological Research (2021
... [Show More] - Semester 1 and Semester 2 - Assignment 2 Answers)
Question & Answers
All answers correct, With Elaborations
Question 1
Why do we calculate a test statistic?
1. To determine whether or not we can accept that the null hypothesis is true
2. To determine how far the observed measurements deviate from what we may expect by chance
3. To get a measurement by which we can calculate the level of significance
4. To determine whether or not we can reject the alternative hypothesis
Answer: Option 2 is correct.
Calculating the test statistic is the first step in a process of comparing the observed data with what may be expected by chance (that is, if in fact the null hypothesis is true and any effects observed in the sample of data are due to random errors).
Option 1 is not really appropriate because the emphasis is wrong here. The test statistic is calculated to determine whether the effect is large enough to reject the null hypothesis and not to try to accept it. For the same reason, Option 4 is not really correct (rejecting the alternative hypothesis would follow only as a consequence of the null hypothesis not being rejected). The level of significance is not calculated but chosen, so Option 3 is false.
Question 2
When applying a statistical test, the probability of a Type I error is equal to the probability of - - - - -.
1. rejecting H0 in error
2. rejecting H1 in error
3. accepting H0 in error
4. not accepting H1 when in fact you should
Answer: Option 1 is correct.
Option 1 is basically a definition of a Type I error. Such an error occurs when a researcher rejects the null hypothesis when it is actually true, and should not have been rejected. The p-value is a direct reflection of the probabily of making this error. (See pp. 84 – 85 in the PYC3704 Guide).
Question 3
A researcher wants to test the hypothesis that the mean depression score on a depression scale for patients diagnosed with clinical depression is greater than 120. The statistical hypothesis to be tested is:
H0: = 120
H1: > 120
She uses a random sample of n=64 drawn from the population of diagnosed patients and finds that ¯x = 127 and s = 24. Which of the values below is the closest to the correct value of s¯x?
1. 0.37
2. 3.0
3. 0.61
4. s¯x cannot be calculated from the information that was provided
Answer: Option 2 gives the correct answer.
This question refers to the standard error of the mean, which is a measurement of how well a sample mean approximates a population mean (see p. 61 in the PYC3704 Guide).
This can be calculated from the data which is provided by substituting the (unknown) population parameters with measurements from the sample (see p. 105 in the Guide where a similar substitution is done), as follows:
Question 4
Suppose the alternative hypothesis states that µ > 60. The researcher should test H0 against H1 if the
- - - - -.
1. sample mean is larger than 60
2. sample mean is smaller than 60
3. sample mean differs from 60, irrespective of the direction of the difference
4. p-value is smaller than the level of significance
Answer: Option 1 is correct.
This is a one-tailed test (see p. 81 in the PYC3704 Guide) where only sample means of larger than 60 are relevant. If the sample mean is calculated and a value of ¯x ≤ 60 is found, the null hypothesis can obviously not be rejected, since there in zero probability that a value of 60 or smaller is also larger than 60. (See p. 77 of the Guide for the discussion of a situation where the observed value of a sample statistic lies in the wrong direction).
Question 5
When applying a t-test for the difference between the means of two independent samples, the probability of obtaining the calculated t-statistic under the null hypothesis is compared to the - - - - - to reach a decision.
1. level of significance
2. degrees of freedom
3. two-tailed probability
4. effect size
Answer: The correct answer is Option 1. [Show Less]