6. Probability and Statistics

Estimation And Testing — Quiz

Test your understanding of estimation and testing with 5 practice questions.

Practice Questions

Question 1

In the context of maximum likelihood estimation (MLE), what is the primary assumption about the observed data?

Question 2

When constructing a confidence interval for a population mean, if the population standard deviation ($\sigma$) is known, which distribution is typically used for the critical values?

Question 3

A researcher is conducting a hypothesis test to evaluate if a new teaching method significantly improves student test scores. The null hypothesis ($H_0$) is that there is no improvement, and the alternative hypothesis ($H_1$) is that there is an improvement. If the researcher sets a significance level ($\alpha$) of $0.05$ and obtains a p-value of $0.03$, what is the correct decision and interpretation?

Question 4

Which of the following scenarios would most likely lead to an increase in the power of a hypothesis test?

Question 5

In Bayesian estimation, if the prior distribution for a parameter $\theta$ is a normal distribution with mean $0$ and variance $1$, and the likelihood function is derived from a set of observations, what does the posterior distribution represent?