MS-DS Master of Data science MS-DS Master of Data science Statistical Inference Concepts Questions and Answers 2 — Questions and Answers
Question 1: In hypothesis testing, what does a Type II error represent?
- Rejecting a true null hypothesis
- Failing to reject a false null hypothesis (Correct answer)
- Rejecting a false null hypothesis
- Failing to reject a true null hypothesis
Correct answer: Failing to reject a false null hypothesis
A Type II error occurs when we fail to reject the null hypothesis even though it is actually false.
Question 2: What is the primary purpose of a confidence interval?
- To determine the exact population parameter
- To provide a range of plausible values for a population parameter (Correct answer)
- To test whether two groups differ significantly
- To calculate the probability of the null hypothesis being true
Correct answer: To provide a range of plausible values for a population parameter
A confidence interval gives a range of values within which the true population parameter is likely to fall based on sample data.
Question 3: Which condition must be satisfied for the Central Limit Theorem to apply to sample means?
- The population must be normally distributed
- The sample size must be sufficiently large regardless of population distribution (Correct answer)
- The population variance must be known
- The sample must be drawn with replacement
Correct answer: The sample size must be sufficiently large regardless of population distribution
The Central Limit Theorem states that the sampling distribution of the mean approaches normality as sample size increases, regardless of the population distribution.
Question 4: What does the power of a statistical test measure?
- The probability of making a Type I error
- The probability of correctly rejecting a false null hypothesis (Correct answer)
- The significance level of the test
- The probability of obtaining the observed data given the null is true
Correct answer: The probability of correctly rejecting a false null hypothesis
Statistical power is the probability of correctly detecting an effect when one truly exists, calculated as 1 minus the Type II error rate.
Question 5: When constructing a likelihood ratio test, what are you comparing?
- The sample mean to the population mean
- The likelihood under the null hypothesis to the likelihood under the alternative (Correct answer)
- The prior probability to the posterior probability
- The observed frequency to the expected frequency
Correct answer: The likelihood under the null hypothesis to the likelihood under the alternative
A likelihood ratio test compares the maximized likelihood under the restricted null model to the maximized likelihood under the full alternative model.
Question 6: What assumption does a paired t-test require about the differences between paired observations?
- The differences follow a uniform distribution
- The differences are approximately normally distributed (Correct answer)
- The variances of both groups are equal
- The observations are independent across pairs
Correct answer: The differences are approximately normally distributed
A paired t-test assumes the differences between paired observations are approximately normally distributed, especially important for small samples.
