PYC3714 Assignment 2 Solutions 2026
UNISA
Psychological Research
Assignment 2 — Semester 2 2026
Full Worked Solutions
Due: Friday, 28 August 2026, 11:00 PM
, Question 1 :Independent-Samples t-Test
1.1 Research hypothesis (directional, in words)
Students who attend extra tutorial sessions will obtain significantly higher exam scores than
students who do not attend extra tutorial sessions.
1.2 Formal statistical hypotheses
H₀: μ₁ ≤ μ₂ (Students who attend extra tutorials do not score higher, on average, than those
who do not.)
H₁: μ₁ > μ₂ (Students who attend extra tutorials score higher, on average, than those who do
not.)
Where μ₁ = population mean exam score for students attending extra tutorials, and μ₂ =
population mean exam score for students not attending extra tutorials. This is a one-tailed
(directional) test.
1.3 Descriptive statistics
Group n Mean (M) SD (s)
Extra tutorials (Group 1) 10 78.70 11.06
No extra tutorials (Group 2) 10 47.10 9.75
1.4 Appropriate statistical test
An independent-samples (unpaired) t-test is appropriate. There are two separate, unrelated
groups of students (tutorial vs no tutorial), the dependent variable (exam score) is measured on
an interval/ratio scale, and we are comparing the means of two independent groups.
1.5 Calculation (step by step)
Step 1 — Pooled variance:
sp² = [(n₁ − 1)s₁² + (n₁ − 1)s₂²] / (n₁ + n₂ − 2)
sp² = [9(11.06)² + 9(9.75)²] / 18 = [9(122.30) + 9(95.06)] / 18 = 1956. = 108.61
Step 2 — Standard error of the difference between means:
SE = √[sp²(1/n₁ + 1/n₂)] = √[108.61(1/10 + 1/10)] = √[108.61 × 0.2] = √21.72 = 4.66
Step 3 — t statistic:
t = (M₁ − M₂) / SE = (78.70 − 47.10) / 4.66 = 31..66 = 6.78
df = n₁ + n₂ − 2 = 10 + 10 − 2 = 18
Calculated statistic: t(18) = 6.78
UNISA
Psychological Research
Assignment 2 — Semester 2 2026
Full Worked Solutions
Due: Friday, 28 August 2026, 11:00 PM
, Question 1 :Independent-Samples t-Test
1.1 Research hypothesis (directional, in words)
Students who attend extra tutorial sessions will obtain significantly higher exam scores than
students who do not attend extra tutorial sessions.
1.2 Formal statistical hypotheses
H₀: μ₁ ≤ μ₂ (Students who attend extra tutorials do not score higher, on average, than those
who do not.)
H₁: μ₁ > μ₂ (Students who attend extra tutorials score higher, on average, than those who do
not.)
Where μ₁ = population mean exam score for students attending extra tutorials, and μ₂ =
population mean exam score for students not attending extra tutorials. This is a one-tailed
(directional) test.
1.3 Descriptive statistics
Group n Mean (M) SD (s)
Extra tutorials (Group 1) 10 78.70 11.06
No extra tutorials (Group 2) 10 47.10 9.75
1.4 Appropriate statistical test
An independent-samples (unpaired) t-test is appropriate. There are two separate, unrelated
groups of students (tutorial vs no tutorial), the dependent variable (exam score) is measured on
an interval/ratio scale, and we are comparing the means of two independent groups.
1.5 Calculation (step by step)
Step 1 — Pooled variance:
sp² = [(n₁ − 1)s₁² + (n₁ − 1)s₂²] / (n₁ + n₂ − 2)
sp² = [9(11.06)² + 9(9.75)²] / 18 = [9(122.30) + 9(95.06)] / 18 = 1956. = 108.61
Step 2 — Standard error of the difference between means:
SE = √[sp²(1/n₁ + 1/n₂)] = √[108.61(1/10 + 1/10)] = √[108.61 × 0.2] = √21.72 = 4.66
Step 3 — t statistic:
t = (M₁ − M₂) / SE = (78.70 − 47.10) / 4.66 = 31..66 = 6.78
df = n₁ + n₂ − 2 = 10 + 10 − 2 = 18
Calculated statistic: t(18) = 6.78
