DAC DAC Statistical Methods & Analytics 2 — Questions and Answers
Question 1: What is the difference between a population and a sample in statistics?
- A population is always smaller than a sample
- A sample is the entire group of interest; a population is a subset used for testing
- A population includes all members of a group; a sample is a subset selected for study (Correct answer)
- There is no meaningful difference between the two terms
Correct answer: A population includes all members of a group; a sample is a subset selected for study
A population is the complete set of all individuals or items of interest, while a sample is a smaller subset drawn from the population for analysis.
Question 2: Which statistical test is appropriate for comparing the means of two independent groups?
- Chi-square test
- Independent samples t-test (Correct answer)
- Pearson correlation
- ANOVA
Correct answer: Independent samples t-test
The independent samples t-test compares the means of two unrelated groups to determine if there is a statistically significant difference.
Question 3: What does a positively skewed distribution indicate about the data?
- Most values are concentrated on the right side with a long left tail
- The mean equals the median
- Most values are concentrated on the left side with a long right tail (Correct answer)
- The data has no outliers
Correct answer: Most values are concentrated on the left side with a long right tail
In a positively skewed distribution, the tail extends to the right, meaning most data values are lower but a few extreme high values pull the mean upward.
Question 4: In regression analysis, what does the R-squared value represent?
- The slope of the regression line
- The proportion of variance in the dependent variable explained by the independent variables (Correct answer)
- The number of variables in the model
- The significance of individual predictors
Correct answer: The proportion of variance in the dependent variable explained by the independent variables
R-squared (coefficient of determination) measures the proportion of variance in the outcome variable that is explained by the predictor variables in the model.
Question 5: What is the purpose of ANOVA (Analysis of Variance)?
- To measure the correlation between two variables
- To compare the means of three or more groups simultaneously (Correct answer)
- To test the normality of a dataset
- To calculate the standard deviation of a sample
Correct answer: To compare the means of three or more groups simultaneously
ANOVA tests whether the means of three or more independent groups are statistically different from each other, using variance within and between groups.
Question 6: Which probability distribution is symmetric and bell-shaped, often used as a basis for statistical inference?
- Poisson distribution
- Exponential distribution
- Binomial distribution
- Normal distribution (Correct answer)
Correct answer: Normal distribution
The normal distribution is a symmetric, bell-shaped continuous probability distribution fundamental to many statistical methods and the Central Limit Theorem.
DAC DAC Statistical Methods & Analytics 2
What is the difference between a population and a sample in statistics?