BSIE Probability & Statistics 3

Question 1

In hypothesis testing, a Type II error occurs when you:

Accepted Answer

Fail to reject a false null hypothesis

Answer

A Type II error (β) is failing to reject H₀ when H₀ is actually false — missing a real effect.

Question 2

A 95% confidence interval for a population mean is calculated as (47.2, 52.8). What is the sample mean?

Accepted Answer

50.0

Answer

The sample mean is the midpoint of the confidence interval: (47.2 + 52.8) / 2 = 50.0.

Question 3

Which probability rule states P(A ∩ B) = P(A) × P(B) when A and B are independent?

Accepted Answer

Multiplication rule

Answer

The multiplication rule for independent events states that the joint probability equals the product of the individual probabilities.

Question 4

For a right-skewed distribution, which inequality is typically true?

Accepted Answer

Mean > Median > Mode

Answer

In a right-skewed distribution, the long right tail pulls the mean above the median, which is above the mode.

Question 5

A random variable X has E[X] = 10 and Var(X) = 4. What is E[3X + 5]?

Accepted Answer

35

Answer

E[3X + 5] = 3·E[X] + 5 = 3(10) + 5 = 35.

BSIE - Bachelor of Science in Industrial Engineering Practice Test