Data Science Data Science Statistical Concepts and Inference Questions and Answers 2

Question 1

A data scientist obtains a 95% confidence interval of (12.3, 18.7) for the population mean. Which interpretation is correct?

Accepted Answer

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

Answer

A 95% confidence interval means that 95% of intervals constructed from repeated samples would capture the true population parameter.

Question 2

Which of the following scenarios would most likely violate the assumption of independence required for a two-sample t-test?

Accepted Answer

Comparing blood pressure readings before and after treatment on the same patients

Answer

Measuring the same patients before and after creates paired observations that are not independent, requiring a paired t-test instead.

Question 3

In hypothesis testing, what does a Type II error represent?

Accepted Answer

Failing to reject a false null hypothesis

Answer

A Type II error occurs when we fail to reject the null hypothesis even though it is actually false, meaning we miss a real effect.

Question 4

A researcher increases the sample size from 50 to 200 while keeping everything else constant. What is the most direct effect on the standard error of the mean?

Accepted Answer

It is cut in half

Answer

Standard error equals sigma divided by the square root of n, so quadrupling n from 50 to 200 halves the standard error.

Question 5

When performing multiple comparisons across 20 groups using individual t-tests at alpha = 0.05, what problem arises?

Accepted Answer

The familywise error rate inflates well beyond 0.05

Answer

Running many pairwise tests without correction inflates the overall probability of at least one false positive far above the nominal alpha level.

Data Science Practice Test

Data Science Practice Test

Data Science Data Science Statistical Concepts and Inference Questions and Answers 2