Data Science Statistical Concepts and Inference 4

Question 1

In Bayesian inference, the posterior distribution is proportional to:

Accepted Answer

The likelihood times the prior

Answer

The prior divided by the likelihood

Answer

The likelihood alone

Answer

The marginal evidence times the posterior

Question 2

A prior distribution in Bayesian analysis represents:

Accepted Answer

Beliefs about a parameter before observing data

Answer

The final estimate after data

Answer

The probability of the data

Answer

The sampling distribution of the estimator

Question 3

Which test is appropriate for comparing the means of two independent groups with continuous outcomes?

Accepted Answer

Independent samples t-test

Answer

Chi-square test

Answer

Pearson correlation

Answer

ANOVA with one group

Question 4

A chi-square test of independence is used to assess:

Accepted Answer

Association between two categorical variables

Answer

Difference between two means

Answer

Linear correlation of two numeric variables

Answer

Equality of variances

Question 5

When should ANOVA be preferred over multiple t-tests?

Accepted Answer

When comparing three or more group means while controlling the family-wise error rate

Answer

When comparing exactly two groups

Answer

When the data are categorical

Answer

When the sample size is below 5

Question 6

A small p-value combined with a tiny effect size in a very large sample suggests:

Accepted Answer

Statistical significance that may lack practical significance

Answer

A large, practically important effect

Answer

An error in the calculation

Answer

That the null hypothesis is certainly false

Question 7

The standard error of the mean decreases as:

Accepted Answer

The sample size increases

Answer

The population variance increases

Answer

The confidence level increases

Answer

The sample size decreases