MS-DS Master of Data science Master of Data science Statistical Inference Concepts 1

Question 1

When performing a two-tailed hypothesis test at a significance level of α = 0.05, what is the critical region in each tail?

Accepted Answer

0.025

Answer

In a two-tailed test, the significance level α is split equally between both tails. With α = 0.05, each tail contains 0.025 of the probability, so the critical region in each tail is 0.025.

Question 2

A researcher increases the sample size in a study while keeping all other factors constant. What is the most likely effect on the width of a 95% confidence interval?

Accepted Answer

The interval becomes narrower

Answer

Increasing sample size reduces the standard error (SE = σ/√n), which directly narrows the margin of error and thus produces a narrower confidence interval, reflecting greater precision.

Question 3

Which of the following best describes a p-value in the context of hypothesis testing?

Accepted Answer

The probability of observing results at least as extreme as the sample data, assuming the null hypothesis is true

Answer

A p-value is the probability of obtaining a test statistic as extreme or more extreme than the one observed, calculated under the assumption that the null hypothesis is true. It does not give the probability that H₀ is true.

Question 4

What happens to the probability of a Type I error if a researcher lowers the significance level from 0.05 to 0.01?

Accepted Answer

It decreases

Answer

The significance level α directly defines the probability of a Type I error (rejecting a true null hypothesis). Lowering α from 0.05 to 0.01 directly reduces the Type I error rate, though it simultaneously increases the risk of a Type II error.

Question 5

In a one-sample z-test, which assumption is required about the population variance?

Accepted Answer

The population variance must be known

Answer

The one-sample z-test requires that the population variance (σ²) is known. When the population variance is unknown and must be estimated from the sample, a t-test is used instead.

MS-DS Master of Data science Practice Test

MS-DS Master of Data science Practice Test

MS-DS Master of Data science Master of Data science Statistical Inference Concepts 1