Master of Data science Statistical Inference Concepts 1 Flashcards
6 cards from real MS-DS Master of Data science practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
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When performing a two-tailed hypothesis test at a significance level of α = 0.05, what is the critical region in each tail?
Answer: 0.025
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.
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?
Answer: The interval becomes narrower
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.
Which of the following best describes a p-value in the context of hypothesis testing?
Answer: The probability of observing results at least as extreme as the sample data, assuming the null hypothesis is true
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.
What happens to the probability of a Type I error if a researcher lowers the significance level from 0.05 to 0.01?
Answer: It decreases
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.
In a one-sample z-test, which assumption is required about the population variance?
Answer: The population variance must be known
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.
A 99% confidence interval is constructed instead of a 95% confidence interval from the same sample. How does this affect the interval?
Answer: It becomes wider and provides greater certainty of capturing the true parameter
Increasing the confidence level from 95% to 99% requires a larger critical value (e.g., z = 2.576 vs 1.96), which widens the interval. The wider interval offers a higher probability (99%) of containing the true population parameter.