chapter 10

Question 1

What is sampling error?

Answer 1

Difference between sample statistic and population parameter (e.g., ȳ − μ, p̂ − p).

Question 2

Formula for SE of the mean (σ known)?

Answer 2

SE(ȳ) = σ / √n

Question 3

Formula for SE of the mean (σ unknown)?

Answer 3

SE(ȳ) = s / √n

Question 4

Formula for SE of a proportion?

Answer 4

SE(p̂) = √(pq / n)

Question 5

What does p̂ stand for?

Answer 5

Sample proportion

Question 6

What does q represent in SE formula?

Answer 6

q = 1 − p

Question 7

Rule for Normal approximation of p̂?

Answer 7

np ≥ 10 and nq ≥ 10

Question 8

What is the CLT?

Answer 8

For large n, sampling distribution ≈ Normal regardless of population shape.

Question 9

Conservative rule for “large n” in CLT?

Answer 9

n ≥ 30

Question 10

Mean of sampling distribution of means?

Answer 10

μ (unbiased estimator)

Question 11

How does SE change with n?

Answer 11

SE decreases as n increases (∝ 1/√n).

Question 12

What is the 10% condition?

Answer 12

n ≤ 10% of population if sampling without replacement.

Question 13

What is the finite population correction (FPC)?

Answer 13

Multiply SE by √((N−n)/(N−1)) if n/N > 0.1

Question 14

Conditions before applying Normal model?

Answer 14

Independence,

Randomization,

10% condition,

For means → n ≥ 30 (or symmetric pop).

For proportions → np ≥ 10, nq ≥ 10.

Question 15

Shape of sample means if population Normal?

Answer 15

Normal distribution.