Shannon Jade Schofield
50393
,Section A: True or False Questions [10 marks]
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
50393
,Section A: True or False Questions [10 marks]
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
