IOP2601 Assignment 3 (COMPLETE ANSWERS) Semester 2
2026 ; 100% correct solutions and explanations.
QUESTION 1
1.1 A Type II error is made by rejecting the null hypothesis when it is in fact true.
Answer: False
Correction: A Type II error occurs when we fail to reject a false null
hypothesis. Rejecting a true null hypothesis is a Type I error.
1.2 ANOVA allows testing for differences across more than two group means and can
evaluate the impact of multiple independent variables.
Answer: True
Explanation: ANOVA (Analysis of Variance) can compare more than two
means, and in factorial ANOVA, it can test the effects of multiple independent
variables as well as their interactions.
1.3 The acronym ANOVA stands for analysis of variables.
Answer: False
Correction: ANOVA stands for Analysis of Variance, not variables.
1.4 A Type I error happens when the null hypothesis is not rejected despite it being
false.
Answer: False
Correction: A Type I error occurs when we reject a true null hypothesis.
Failing to reject a false null hypothesis is a Type II error.
1.5 The Chi-Square test is typically used to assess the association between two
categorical variables.
, Answer: True
Explanation: The Chi-Square test of independence is commonly used to test
whether two categorical variables are associated.
QUESTION 2
2.1 Null vs alternative hypothesis — explanation + example (4)
Null hypothesis (H₀): a statement of no effect or no difference; it is the hypothesis we
test directly and assume true until evidence suggests otherwise. The null is what we
attempt to reject using sample data.
Alternative hypothesis (H₁ or Hₐ): the statement that there is an effect, difference, or
relationship. It represents the researcher’s claim or what they want to provide
evidence for.
Key differences
H₀ expresses no-change / no-difference; H₁ expresses the presence of change or
difference.
Statistical tests produce a probability (p-value) assuming H₀ is true; if p is small
enough we reject H₀ in favour of H₁.
Type I error = rejecting a true H₀; Type II error = failing to reject a false H₀.
Example: A school principal claims a new teaching method does not change average
test scores.
H₀: μ_new = μ_old (no difference in mean scores)
H₁: μ_new ≠ μ_old (the new method changes mean scores)
If sample data provide strong evidence (small p-value) against H₀, we reject H₀
and conclude the new method likely changes scores.
Reference (APA): Gravetter, F. J., & Wallnau, L. B. (2017). Statistics for the
Behavioral Sciences (10th ed.). Cengage.
2026 ; 100% correct solutions and explanations.
QUESTION 1
1.1 A Type II error is made by rejecting the null hypothesis when it is in fact true.
Answer: False
Correction: A Type II error occurs when we fail to reject a false null
hypothesis. Rejecting a true null hypothesis is a Type I error.
1.2 ANOVA allows testing for differences across more than two group means and can
evaluate the impact of multiple independent variables.
Answer: True
Explanation: ANOVA (Analysis of Variance) can compare more than two
means, and in factorial ANOVA, it can test the effects of multiple independent
variables as well as their interactions.
1.3 The acronym ANOVA stands for analysis of variables.
Answer: False
Correction: ANOVA stands for Analysis of Variance, not variables.
1.4 A Type I error happens when the null hypothesis is not rejected despite it being
false.
Answer: False
Correction: A Type I error occurs when we reject a true null hypothesis.
Failing to reject a false null hypothesis is a Type II error.
1.5 The Chi-Square test is typically used to assess the association between two
categorical variables.
, Answer: True
Explanation: The Chi-Square test of independence is commonly used to test
whether two categorical variables are associated.
QUESTION 2
2.1 Null vs alternative hypothesis — explanation + example (4)
Null hypothesis (H₀): a statement of no effect or no difference; it is the hypothesis we
test directly and assume true until evidence suggests otherwise. The null is what we
attempt to reject using sample data.
Alternative hypothesis (H₁ or Hₐ): the statement that there is an effect, difference, or
relationship. It represents the researcher’s claim or what they want to provide
evidence for.
Key differences
H₀ expresses no-change / no-difference; H₁ expresses the presence of change or
difference.
Statistical tests produce a probability (p-value) assuming H₀ is true; if p is small
enough we reject H₀ in favour of H₁.
Type I error = rejecting a true H₀; Type II error = failing to reject a false H₀.
Example: A school principal claims a new teaching method does not change average
test scores.
H₀: μ_new = μ_old (no difference in mean scores)
H₁: μ_new ≠ μ_old (the new method changes mean scores)
If sample data provide strong evidence (small p-value) against H₀, we reject H₀
and conclude the new method likely changes scores.
Reference (APA): Gravetter, F. J., & Wallnau, L. B. (2017). Statistics for the
Behavioral Sciences (10th ed.). Cengage.
