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

There is a 95% probability the population mean lies in this interval

Answer

95% of sample means fall in this interval

Answer

The sample mean has a 95% chance of being between 12.3 and 18.7

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

Comparing test scores of students from two different schools

Answer

Comparing heights of randomly selected men and women

Answer

Comparing salaries from two different industries

Question 3

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

Accepted Answer

Failing to reject a false null hypothesis

Answer

Rejecting a true null hypothesis

Answer

Rejecting a false null hypothesis

Answer

Failing to reject a true null hypothesis

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

It is reduced by a factor of four

Answer

It doubles

Answer

It remains the same

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

The power of each test decreases to near zero

Answer

The sample size requirement increases exponentially

Answer

The effect size becomes undetectable

Question 6

Which measure of central tendency is most robust to outliers in a skewed dataset?

Accepted Answer

Median

Answer

Arithmetic mean

Answer

Geometric mean

Answer

Variance