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

95% of the data falls within the interval

Answer

There is a 95% probability the sample mean is correct

Answer

The interval contains 95% of all possible sample means

Question 2

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

Accepted Answer

Increasing the population variance

Answer

Increasing the sample size

Answer

Decreasing the confidence level

Answer

Reducing the standard error

Question 3

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

Accepted Answer

Rejecting a true null hypothesis

Answer

Failing to reject a false null hypothesis

Answer

Accepting the alternative when it is false because of low power

Answer

Using the wrong test statistic

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

The probability the null hypothesis is true

Answer

The probability the alternative hypothesis is true

Answer

The size of the effect being tested

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

Uniform regardless of population shape

Answer

Identical to the population distribution

Answer

Exponential for skewed populations

Question 6

Statistical power is the probability of:

Accepted Answer

Rejecting the null when the alternative is actually true

Answer

Failing to reject a true null

Answer

Making a Type I error

Answer

Obtaining a statistically significant result by chance

Question 7

Which factor does NOT increase statistical power?

Accepted Answer

Smaller significance level (alpha)

Answer

Larger sample size

Answer

Larger true effect size

Answer

Lower measurement variance