Data Science Data Science Statistical Concepts and Inference Questions and Answers 3

Question 1

A machine learning model yields a p-value of 0.03 when testing whether a new feature improves prediction accuracy. With alpha = 0.01, what is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis because 0.03 > 0.01

Answer

Reject the null hypothesis because 0.03 is small

Answer

Accept the alternative hypothesis

Answer

The test is inconclusive and must be repeated

Question 2

What does the Central Limit Theorem guarantee about the sampling distribution of the sample mean?

Accepted Answer

It approaches a normal distribution as sample size increases, regardless of population shape

Answer

It will be uniform for any sample size

Answer

It equals the population distribution exactly

Answer

It will be skewed if the population is skewed

Question 3

In Bayesian inference, what role does the prior distribution play?

Accepted Answer

It encodes beliefs about a parameter before observing data

Answer

It represents the likelihood of the observed data

Answer

It is the final output of the analysis

Answer

It measures the frequency of Type I errors

Question 4

A correlation coefficient of r = -0.92 between two variables indicates which of the following?

Accepted Answer

A strong negative linear relationship

Answer

A weak positive linear relationship

Answer

No meaningful relationship

Answer

A causal relationship where one variable decreases the other

Question 5

Which resampling technique estimates the variability of a statistic by repeatedly sampling with replacement from the observed data?

Accepted Answer

Bootstrap

Answer

Cross-validation

Answer

Permutation test

Answer

Jackknife

Question 6

When is the chi-squared test of independence most appropriate?

Accepted Answer

Testing whether two categorical variables are associated

Answer

Comparing means of two continuous variables

Answer

Estimating regression coefficients

Answer

Measuring the variance of a single continuous variable