Module 5 Quiz – Sampling Distributions

Quiz Instructions

Answer all 15 multiple-choice questions
You need 11 out of 15 (70%) correct to pass
You'll receive immediate feedback with explanations
You can retake the quiz as many times as needed

Question 1

Which of the following is a population parameter?

a) x̄ = 75 (sample mean)

b) μ = 80 (population mean)

c) s = 10 (sample standard deviation)

d) p̂ = 0.52 (sample proportion)

Question 2

A sampling distribution is:

a) The distribution of individual values in one sample

b) The distribution of a statistic (like x̄) from all possible samples of size n

c) The method used to collect a random sample

d) The distribution of the entire population

Question 3

The Central Limit Theorem states that for large samples (n ≥ 30), the sampling distribution of x̄ is:

a) Exactly the same shape as the population

b) Approximately normal, regardless of the population shape

c) Uniform

d) Always skewed to the right

Question 4

If a population has mean μ = 50, what is the mean of the sampling distribution of x̄ (for any sample size)?

a) It depends on the sample size

b) μₓ̄ = 50

c) Cannot be determined without knowing σ

d) μₓ̄ = 50/√n

Question 5

If σ = 20 and n = 100, what is the standard error of x̄?

a) SE = 20

b) SE = 2

c) SE = 0.2

d) SE = 200

Question 6

A population has μ = 60 and σ = 12. For samples of n = 36, what is P(x̄ > 63)?

a) About 1.5%

b) About 6.7%

c) About 15.9%

d) About 40.1%

Question 7

To reduce the standard error by half, you must:

a) Double the sample size

b) Quadruple the sample size

c) Halve the sample size

d) Increase sample size by √2

Question 8

What is the difference between standard deviation (σ) and standard error (SE)?

a) They are the same thing

b) σ measures variability of individuals; SE measures variability of sample means

c) SE is always larger than σ

d) σ is for samples; SE is for populations

Question 9

In a sample of 200 people, 80 prefer product A. What is the sample proportion p̂?

a) p̂ = 0.80

b) p̂ = 0.40

c) p̂ = 0.60

d) p̂ = 0.20

Question 10

For normal approximation of p̂ to be appropriate, which conditions must be met?

a) n ≥ 30

b) np ≥ 10 AND n(1-p) ≥ 10

c) p = 0.5

d) The population must be normally distributed

Question 11

If p = 0.3 and n = 100, what is the standard error of p̂?

a) SE ≈ 0.046

b) SE ≈ 0.03

c) SE ≈ 0.3

d) SE ≈ 0.0021

Question 12

The Central Limit Theorem does NOT apply when:

a) The population is normally distributed and n = 20

b) The population is highly skewed and n = 10

c) The population is uniform and n = 50

d) The population is bimodal and n = 100

Question 13

Nationally, 40% of adults exercise regularly. In a sample of 100 adults, approximately what is P(p̂ < 0.35)?

a) About 15%

b) About 35%

c) About 50%

d) About 65%

Question 14

A population has μ = 100 and σ = 20. Which is more likely: one individual having a value above 120, or the mean of 25 individuals exceeding 120?

a) One individual above 120 is more likely

b) Mean of 25 exceeding 120 is more likely

c) Both are equally likely

d) Cannot determine without more information

Question 15

A company claims the average customer wait time is μ = 5 minutes with σ = 2 minutes. A sample of 64 customers has x̄ = 5.5 minutes. If the claim is true, approximately what is P(x̄ ≥ 5.5)?

a) About 2.3%

b) About 5.0%

c) About 15.9%

d) About 30.9%