This is a final exam including questions and answers for Introduction to Research Methods and Statistics. The final grade received for this exam was 92% for which I received a distinction.
1. We cannot use Pearson correlation with variables measured at a nominal or ordinal scale.
2. A score with a value less than or equal to the mean will have a z-score that is less than or equal to zero.
3. One reason for transforming X values into z-scores is that the set of z-scores will form a normal shaped
distribution.
4. If an entire population with μ = 40 and σ = 7 is transformed into z-scores, then the distribution of z-scores will
have a mean of 0 and a standard deviation of 1.
5. The null hypothesis is stated in terms of the population, even though the data come from a sample.
6. It is impossible to have a correlation coefficient value of 2.33.
7. If the obtained sample mean is located in the critical region, then your decision should be to "reject H 0.”
8. A Type II error occurs when you conclude that a treatment effect exists, but the treatment has no effect.
9. A positive z-score always corresponds to an X value greater than the mean.
10. For any population, a z-score of +1.00 corresponds to a location exactly 10 points above the mean.
____________________________________________________________________________
Section B: Calculations [90 marks]
1. Books in the Cornerstone library are found to have a mean length of =450 pages with a standard deviation
of σ= 100 pages. What is the z-score corresponding to a book of the following length? (10 Marks)
a. 180 pages
b. 380 pages
c. 515 pages
d. 400 pages
e. 640 pages
2. A normal distribution of scores has a variance of S2=100. Find the z-scores corresponding to each of the
following values: (10 Marks)
a. A score that is 20 points above the mean.
b. A score that is 10 points below the mean.
c. A score that is 15 points above the mean
d. A score that is 30 points below the mean.
e. A score that is 5 points above the mean.
3. Given a mean score of 43 and a standard deviation of 5 for ‘Teaching readiness test’ among a sample of
PGCE students from Cornerstone, calculate raw scores for the following; (10 Marks)
a. A z-score of 1.50
b. A z-score of -2.00
c. A z-score of -1.20
d. A z-score of 1.30
e. A z-score of -0.80
4. Subjective wellbeing was measured among a sample of Statistics students, with M = 150 and S 2 = 25. Determine the z
scores for the students who obtained the following scores on the subjective wellbeing measure. (5 Marks)
, a. 110
b. 135
5. A normal distribution has μ = 80 and σ = 10. What is the probability of randomly selecting the following
scores? (10 Marks)
a. X > 75
b. X < 85
c. Between the mean and a score of 90
d. Between the mean and a score of 50
e. 75 < X < 85
6. Determine the z-score value in each of the following scenarios: (6 Marks)
a. What z-score value separates the top 8% of a normal distribution from the bottom 92%?
b. What z-score value separates the top 72% of a normal distribution from the bottom 28%?
c. What z-scores values represents the middle 90% of the values in a normal distribution?
7. The Welcher Adult Intelligence Test Scale is composed of several subtests. On one subtest, the raw scores have a
mean of 55 and a variance of 25. Assuming these raw scores are form a normal distribution;
a. What is the probability of obtaining a raw score between the mean and 46? (3 Marks)
b. What is the probability of obtaining a raw score between 50 and 58? (6 Marks)
8. The Research Methods and Statistic module is almost over. Assume that the total marks were at an average
of μ= 18 per assessment, and that the distribution of total marks are normally distributed with σ= 10.
a. What is the proportion that a student would have a mark more than 24 mark if randomly selected? (4)
b. What proportion of students would have marks between 10 and 24? (6)
9. It is believed that there is a relationship between ‘level of information’ and ‘readiness to take a vaccination
jab’ among tertiary institution students. To test this relationship, a research team decides to conduct a study
using a sample of tertiary students.
Level of information Readiness score
7 7
9 6
9 6
2 3
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller shannonschofield. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R130,00. You're not tied to anything after your purchase.
