Data and Analytics Statistical Analysis 2 — Questions and Answers
Question 1: What is the Central Limit Theorem (CLT)?
- The mean always equals the median in a dataset
- The sampling distribution of the mean approaches normal as sample size increases (Correct answer)
- Larger datasets always have smaller standard deviations
- All populations follow a normal distribution
Correct answer: The sampling distribution of the mean approaches normal as sample size increases
The CLT states that the sampling distribution of the sample mean approximates a normal distribution as sample size increases, regardless of population distribution.
Question 2: What does R-squared (R²) measure in regression analysis?
- The slope of the regression line
- The proportion of variance in the dependent variable explained by the model (Correct answer)
- The statistical significance of the model
- The number of predictors in the model
Correct answer: The proportion of variance in the dependent variable explained by the model
R-squared measures the proportion of variance in the dependent variable that is explained by the independent variable(s) in the model.
Question 3: What is the interquartile range (IQR)?
- The difference between max and min values
- The difference between the 75th and 25th percentiles (Correct answer)
- The average of Q1 and Q3
- The standard deviation of the middle 50% of data
Correct answer: The difference between the 75th and 25th percentiles
The IQR is Q3 minus Q1, representing the spread of the middle 50% of data and used to identify outliers.
Question 4: Which statistical test compares means across more than two independent groups?
- t-test
- Chi-square test
- ANOVA (Correct answer)
- Pearson correlation
Correct answer: ANOVA
ANOVA (Analysis of Variance) tests whether the means of three or more independent groups are significantly different.
Question 5: What is a confidence interval?
- The range within which the sample mean falls
- A range of values likely to contain the true population parameter (Correct answer)
- The probability that a hypothesis is correct
- The margin of error in data collection
Correct answer: A range of values likely to contain the true population parameter
A confidence interval provides a range of plausible values for a population parameter with a specified level of confidence (e.g., 95%).
Question 6: What is multicollinearity in regression analysis?
- Using multiple outcome variables
- High correlation among independent predictor variables (Correct answer)
- Non-linear relationships between variables
- Unequal variance across residuals
Correct answer: High correlation among independent predictor variables
Multicollinearity occurs when two or more independent variables in a regression model are highly correlated, making it difficult to isolate individual effects.
Data and Analytics Statistical Analysis 2
What is the Central Limit Theorem (CLT)?