Data Science Statistical Concepts and Inference 2

Question 1

A 95% confidence interval for a population mean means which of the following?

Accepted Answer

If we repeated sampling many times, about 95% of such intervals would contain the true mean

Answer

A confidence level refers to the long-run proportion of constructed intervals that capture the true parameter, not the probability for a single fixed interval.

Question 2

Which of the following increases the width of a confidence interval, all else equal?

Accepted Answer

Increasing the population variance

Answer

Greater population variance increases the standard error, widening the interval.

Question 3

A Type I error in hypothesis testing is best described as:

Accepted Answer

Rejecting a true null hypothesis

Answer

A Type I error is a false positive: rejecting a null hypothesis that is actually true.

Question 4

What does the p-value represent?

Accepted Answer

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

Answer

A p-value is the probability of results as or more extreme than observed under the assumption the null hypothesis holds.

Question 5

The Central Limit Theorem states that, for a large sample size, the sampling distribution of the sample mean is approximately:

Accepted Answer

Normal regardless of population distribution

Answer

The CLT guarantees the sample mean's distribution approaches normality as sample size grows, no matter the population shape.

Data Science Practice Test

Data Science Practice Test

Data Science Statistical Concepts and Inference 2