Comprehensive Statistics Exam Questions
and Answers 2026/2027: Normal
Distribution, Correlation, Regression,
Hypothesis Testing, ANOVA and Chi-Square
Practice Test with Fully Worked Solutions
for University Students
Description:
Prepare for your 2026/2027 statistics exam with this comprehensive test bank covering normal
distribution, Z-scores, probability, Pearson correlation, linear regression, hypothesis
testing, t-tests, ANOVA, and chi-square tests. Includes 105 multiple-choice questions with
detailed worked explanations, a formula reference sheet, difficulty labels, and a consolidated
answer key. Perfect for university exam prep, study guides, and digital learning.
Download your complete statistics practice exam with answers today and walk into your exam fully
prepared.
, Course Code: STAT 2026-B
Academic Year: 2026/2027
Duration: 4 Hours
Total Marks: 150
Instructions to Candidates
This examination paper consists of six sections. Answer all questions. All questions are of equal
value unless otherwise stated. A standard normal distribution table (Z-table), t-distribution table,
F-distribution table, and chi-square distribution table are provided. A basic calculator is
permitted.
Formula Reference Sheet
Descriptive Statistics
Mean: M = ΣX / n
Sum of Squares: SS = Σ(X - M)²
Variance: s² = SS / (n - 1)
Standard Deviation: s = √s²
Normal Distribution
Z-score transformation: Z = (X - µ) / σ
X from Z-score: X = µ + (Z)(σ)
Correlation
Pearson correlation: r = SP / √(SSx × SSy)
Sum of Products: SP = Σ(X - Mx)(Y - My)
Sum of Squares for X: SSx = Σ(X - Mx)²
Sum of Squares for Y: SSy = Σ(Y - My)²
Coefficient of determination: r²
, Linear Regression
Regression equation: Ŷ = bX + a
Slope: b = SP / SSx
Y-intercept: a = My - b(Mx)
Hypothesis Testing
One-sample t-test: t = (M - µ) / (s / √n)
Independent-samples t-test: t = (M₁ - M₂) / √(s²p/n₁ + s²p/n₂)
Pooled variance: s²p = (SS₁ + SS₂) / (df₁ + df₂)
Paired-samples t-test: t = MD / (sD / √n)
Degrees of freedom (one-sample): df = n - 1
Degrees of freedom (independent): df = n₁ + n₂ - 2
Degrees of freedom (paired): df = n - 1
ANOVA
F-ratio: F = MSbetween / MSwithin
SSbetween = Σ(nk × (Mk - Mgrand)²)
SSwithin = ΣSSk
SStotal = SSbetween + SSwithin
dfbetween = k - 1
dfwithin = N - k
MSbetween = SSbetween / dfbetween
MSwithin = SSwithin / dfwithin
Chi-Square
Chi-square goodness of fit: χ² = Σ((O - E)² / E)
Chi-square test of independence: χ² = Σ((O - E)² / E)
Degrees of freedom (goodness of fit): df = k - 1
Degrees of freedom (independence): df = (r - 1)(c - 1)
, Effect Size
Cohen's d: d = (M₁ - M₂) / s
Cohen's guidelines for d: 0.20 (small), 0.50 (medium), 0.80 (large)
Cohen's guidelines for r: 0.10 (small), 0.30 (medium), 0.50 (large)
and Answers 2026/2027: Normal
Distribution, Correlation, Regression,
Hypothesis Testing, ANOVA and Chi-Square
Practice Test with Fully Worked Solutions
for University Students
Description:
Prepare for your 2026/2027 statistics exam with this comprehensive test bank covering normal
distribution, Z-scores, probability, Pearson correlation, linear regression, hypothesis
testing, t-tests, ANOVA, and chi-square tests. Includes 105 multiple-choice questions with
detailed worked explanations, a formula reference sheet, difficulty labels, and a consolidated
answer key. Perfect for university exam prep, study guides, and digital learning.
Download your complete statistics practice exam with answers today and walk into your exam fully
prepared.
, Course Code: STAT 2026-B
Academic Year: 2026/2027
Duration: 4 Hours
Total Marks: 150
Instructions to Candidates
This examination paper consists of six sections. Answer all questions. All questions are of equal
value unless otherwise stated. A standard normal distribution table (Z-table), t-distribution table,
F-distribution table, and chi-square distribution table are provided. A basic calculator is
permitted.
Formula Reference Sheet
Descriptive Statistics
Mean: M = ΣX / n
Sum of Squares: SS = Σ(X - M)²
Variance: s² = SS / (n - 1)
Standard Deviation: s = √s²
Normal Distribution
Z-score transformation: Z = (X - µ) / σ
X from Z-score: X = µ + (Z)(σ)
Correlation
Pearson correlation: r = SP / √(SSx × SSy)
Sum of Products: SP = Σ(X - Mx)(Y - My)
Sum of Squares for X: SSx = Σ(X - Mx)²
Sum of Squares for Y: SSy = Σ(Y - My)²
Coefficient of determination: r²
, Linear Regression
Regression equation: Ŷ = bX + a
Slope: b = SP / SSx
Y-intercept: a = My - b(Mx)
Hypothesis Testing
One-sample t-test: t = (M - µ) / (s / √n)
Independent-samples t-test: t = (M₁ - M₂) / √(s²p/n₁ + s²p/n₂)
Pooled variance: s²p = (SS₁ + SS₂) / (df₁ + df₂)
Paired-samples t-test: t = MD / (sD / √n)
Degrees of freedom (one-sample): df = n - 1
Degrees of freedom (independent): df = n₁ + n₂ - 2
Degrees of freedom (paired): df = n - 1
ANOVA
F-ratio: F = MSbetween / MSwithin
SSbetween = Σ(nk × (Mk - Mgrand)²)
SSwithin = ΣSSk
SStotal = SSbetween + SSwithin
dfbetween = k - 1
dfwithin = N - k
MSbetween = SSbetween / dfbetween
MSwithin = SSwithin / dfwithin
Chi-Square
Chi-square goodness of fit: χ² = Σ((O - E)² / E)
Chi-square test of independence: χ² = Σ((O - E)² / E)
Degrees of freedom (goodness of fit): df = k - 1
Degrees of freedom (independence): df = (r - 1)(c - 1)
, Effect Size
Cohen's d: d = (M₁ - M₂) / s
Cohen's guidelines for d: 0.20 (small), 0.50 (medium), 0.80 (large)
Cohen's guidelines for r: 0.10 (small), 0.30 (medium), 0.50 (large)
