MS-DS Master of Data science MS-DS Master of Data science Statistical Inference Concepts Questions and Answers 2

Question 1

In hypothesis testing, what does a Type II error represent?

Accepted Answer

Failing to reject a false null hypothesis

Answer

Rejecting a true null hypothesis

Answer

Rejecting a false null hypothesis

Answer

Failing to reject a true null hypothesis

Question 2

What is the primary purpose of a confidence interval?

Accepted Answer

To provide a range of plausible values for a population parameter

Answer

To determine the exact population parameter

Answer

To test whether two groups differ significantly

Answer

To calculate the probability of the null hypothesis being true

Question 3

Which condition must be satisfied for the Central Limit Theorem to apply to sample means?

Accepted Answer

The sample size must be sufficiently large regardless of population distribution

Answer

The population must be normally distributed

Answer

The population variance must be known

Answer

The sample must be drawn with replacement

Question 4

What does the power of a statistical test measure?

Accepted Answer

The probability of correctly rejecting a false null hypothesis

Answer

The probability of making a Type I error

Answer

The significance level of the test

Answer

The probability of obtaining the observed data given the null is true

Question 5

When constructing a likelihood ratio test, what are you comparing?

Accepted Answer

The likelihood under the null hypothesis to the likelihood under the alternative

Answer

The sample mean to the population mean

Answer

The prior probability to the posterior probability

Answer

The observed frequency to the expected frequency

Question 6

What assumption does a paired t-test require about the differences between paired observations?

Accepted Answer

The differences are approximately normally distributed

Answer

The differences follow a uniform distribution

Answer

The variances of both groups are equal

Answer

The observations are independent across pairs