Data Science Statistical Concepts and Analysis 2 — Questions and Answers
Question 1: A dataset of household incomes has a few extreme high values. Which measure of central tendency is LEAST affected by these outliers?
- Median (Correct answer)
- Mean
- Range
- Standard deviation
Correct answer: Median
The median is based on rank position, so extreme values do not pull it like they pull the mean.
Question 2: A p-value of 0.03 in a test with significance level 0.05 means:
- Reject the null hypothesis (Correct answer)
- Fail to reject the null hypothesis
- The null hypothesis is true
- The effect size is large
Correct answer: Reject the null hypothesis
When the p-value is below alpha, the result is statistically significant and the null hypothesis is rejected.
Question 3: Which statement best describes the Central Limit Theorem?
- The sampling distribution of the mean approaches normality as sample size grows (Correct answer)
- All data become normal with enough samples
- Variance shrinks to zero with large samples
- The population mean equals the sample mean exactly
Correct answer: The sampling distribution of the mean approaches normality as sample size grows
The CLT states the distribution of sample means tends toward normal regardless of the population shape as n increases.
Question 4: A correlation coefficient of -0.85 between two variables indicates:
- A strong negative linear relationship (Correct answer)
- A weak negative relationship
- No relationship
- A strong positive relationship
Correct answer: A strong negative linear relationship
Values near -1 indicate a strong inverse linear association.
Question 5: What does a 95% confidence interval for a mean actually represent?
- A range that would contain the true mean in 95% of repeated samples (Correct answer)
- A 95% probability the sample mean is correct
- 95% of the data fall within the interval
- The mean is exactly in the center 95% of the time
Correct answer: A range that would contain the true mean in 95% of repeated samples
The confidence level refers to the long-run proportion of such intervals capturing the true parameter.
Question 6: Which type of error occurs when you reject a null hypothesis that is actually true?
- Type I error (Correct answer)
- Type II error
- Sampling error
- Measurement error
Correct answer: Type I error
A Type I error is a false positive—rejecting a true null hypothesis.
Question 7: A distribution with a long tail extending to the right is described as:
- Right-skewed (positively skewed) (Correct answer)
- Left-skewed (negatively skewed)
- Symmetric
- Bimodal
Correct answer: Right-skewed (positively skewed)
A tail pointing toward higher values indicates positive (right) skew, with mean greater than median.
Data Science Statistical Concepts and Analysis 2
A dataset of household incomes has a few extreme high values.
Which measure of central tendency is LEAST affected by these outliers?