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QMB 3200 Business Statistics Final
Exam | ANOVA, Regression, Chi-Square,
Hypothesis Testing | Multiple Choice &
Open-Ended Q&A | Verified Answers
Exam Structure:
Subject: Business Statistics – ANOVA, Regression, & Chi-Square (QMB 3200)
Source: QMB 3200 Final Exam Test – Verified Answers
Format: Multiple Choice & Open-Ended Q&A
1. What are treatments in the context of ANOVA?
Correct Answer: Different levels of a factor.
Rationale:
1. Treatments are the specific conditions applied to experimental units.
2. For example, if factor is “drug dosage,” treatments might be 0 mg, 50 mg,
and 100 mg.
3. The term is commonly used in ANOVA to refer to the populations being
compared.
4. Different treatments allow researchers to test for differences in response
means.
2. What is the response variable?
Correct Answer: Another word for the dependent variable of interest.
Rationale:
1. The response variable measures the outcome of an experiment.
2. It is what is being predicted or explained.
3. In ANOVA, the response variable is quantitative (continuous).
4. The response variable changes based on different levels of the factor(s).
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3. What is a factor in ANOVA?
Correct Answer: Another word for the independent variable of interest.
Rationale:
1. A factor is a categorical variable that defines the groups being compared.
2. It is the independent variable that researchers manipulate or observe.
3. Examples include: “brand,” “teaching method,” or “diet type.”
4. Factors can have multiple levels (treatments).
4. What is an ANOVA table?
Correct Answer: A table used to summarize the analysis of variance
computations and results. It contains columns showing the source of
variation, the sum of squares, the degrees of freedom, the mean square, the
F value(s), and the p-value(s).
Rationale:
1. The ANOVA table organizes variance components into systematic groups.
2. Sources of variation typically include treatment (between groups) and
error (within groups).
3. The F-statistic is calculated as the ratio of mean squares (MSTR/MSE).
4. The p-value determines statistical significance of the factor.
5. What is Analysis of Variance (ANOVA)?
Correct Answer: A statistical method that can be used to test for equality
of three or more population means.
Rationale:
1. ANOVA extends the t-test for two means to three or more groups.
2. The null hypothesis is that all population means are equal (H₀: μ₁ = μ₂ =
... = μₖ).
3. The alternative hypothesis is that at least one mean is different.
4. It analyzes variance within and between samples to make inferences about
means.
6. What is SSE (Sum of Squares Due to Error)?
Correct Answer: Sum of squares due to error.
Rationale:
1. SSE measures the variability within each treatment group.
2. It represents the random or unexplained variation.
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3. It is calculated as the sum of squared deviations of each observation from
its own sample mean.
4. In ANOVA, SSE is used in the denominator of the F-test (MSE = SSE /
dfE).
7. What is SSTR (Sum of Squares Due to Treatments)?
Correct Answer: Sum of squares due to treatments.
Rationale:
1. SSTR measures the variability between treatment group means.
2. It represents the explained variation due to the factor.
3. It is calculated as the sum of squared deviations of each sample mean from
the overall mean, weighted by sample size.
4. In ANOVA, SSTR is used in the numerator of the F-test (MSTR = SSTR /
dfTR).
8. What is the point estimator for the difference between two
population means?
Correct Answer: x̄ ₁ – x̄ ₂.
Rationale:
1. The sample mean difference is an unbiased estimator of the population
mean difference.
2. It is used in both t-tests and z-tests for comparing two means.
3. The estimator’s variability is measured by the standard error.
4. Confidence intervals and hypothesis tests rely on this estimator.
9. What does the standard error of x̄ ₁ – x̄ ₂ describe?
Correct Answer: The variation in the sampling distribution of the
estimator.
Rationale:
1. The standard error measures how much the sample mean difference varies
from sample to sample.
2. It is calculated as √(σ₁²/n₁ + σ₂²/n₂) when variances are known.
3. A smaller standard error indicates a more precise estimate of the
difference.
4. It is used to construct confidence intervals and test statistics.
QMB 3200 Business Statistics Final
Exam | ANOVA, Regression, Chi-Square,
Hypothesis Testing | Multiple Choice &
Open-Ended Q&A | Verified Answers
Exam Structure:
Subject: Business Statistics – ANOVA, Regression, & Chi-Square (QMB 3200)
Source: QMB 3200 Final Exam Test – Verified Answers
Format: Multiple Choice & Open-Ended Q&A
1. What are treatments in the context of ANOVA?
Correct Answer: Different levels of a factor.
Rationale:
1. Treatments are the specific conditions applied to experimental units.
2. For example, if factor is “drug dosage,” treatments might be 0 mg, 50 mg,
and 100 mg.
3. The term is commonly used in ANOVA to refer to the populations being
compared.
4. Different treatments allow researchers to test for differences in response
means.
2. What is the response variable?
Correct Answer: Another word for the dependent variable of interest.
Rationale:
1. The response variable measures the outcome of an experiment.
2. It is what is being predicted or explained.
3. In ANOVA, the response variable is quantitative (continuous).
4. The response variable changes based on different levels of the factor(s).
, 2|Page
3. What is a factor in ANOVA?
Correct Answer: Another word for the independent variable of interest.
Rationale:
1. A factor is a categorical variable that defines the groups being compared.
2. It is the independent variable that researchers manipulate or observe.
3. Examples include: “brand,” “teaching method,” or “diet type.”
4. Factors can have multiple levels (treatments).
4. What is an ANOVA table?
Correct Answer: A table used to summarize the analysis of variance
computations and results. It contains columns showing the source of
variation, the sum of squares, the degrees of freedom, the mean square, the
F value(s), and the p-value(s).
Rationale:
1. The ANOVA table organizes variance components into systematic groups.
2. Sources of variation typically include treatment (between groups) and
error (within groups).
3. The F-statistic is calculated as the ratio of mean squares (MSTR/MSE).
4. The p-value determines statistical significance of the factor.
5. What is Analysis of Variance (ANOVA)?
Correct Answer: A statistical method that can be used to test for equality
of three or more population means.
Rationale:
1. ANOVA extends the t-test for two means to three or more groups.
2. The null hypothesis is that all population means are equal (H₀: μ₁ = μ₂ =
... = μₖ).
3. The alternative hypothesis is that at least one mean is different.
4. It analyzes variance within and between samples to make inferences about
means.
6. What is SSE (Sum of Squares Due to Error)?
Correct Answer: Sum of squares due to error.
Rationale:
1. SSE measures the variability within each treatment group.
2. It represents the random or unexplained variation.
, 3|Page
3. It is calculated as the sum of squared deviations of each observation from
its own sample mean.
4. In ANOVA, SSE is used in the denominator of the F-test (MSE = SSE /
dfE).
7. What is SSTR (Sum of Squares Due to Treatments)?
Correct Answer: Sum of squares due to treatments.
Rationale:
1. SSTR measures the variability between treatment group means.
2. It represents the explained variation due to the factor.
3. It is calculated as the sum of squared deviations of each sample mean from
the overall mean, weighted by sample size.
4. In ANOVA, SSTR is used in the numerator of the F-test (MSTR = SSTR /
dfTR).
8. What is the point estimator for the difference between two
population means?
Correct Answer: x̄ ₁ – x̄ ₂.
Rationale:
1. The sample mean difference is an unbiased estimator of the population
mean difference.
2. It is used in both t-tests and z-tests for comparing two means.
3. The estimator’s variability is measured by the standard error.
4. Confidence intervals and hypothesis tests rely on this estimator.
9. What does the standard error of x̄ ₁ – x̄ ₂ describe?
Correct Answer: The variation in the sampling distribution of the
estimator.
Rationale:
1. The standard error measures how much the sample mean difference varies
from sample to sample.
2. It is calculated as √(σ₁²/n₁ + σ₂²/n₂) when variances are known.
3. A smaller standard error indicates a more precise estimate of the
difference.
4. It is used to construct confidence intervals and test statistics.
