Stats

What are all possible samples of size 2 with replacement from 4K, 2K, 3K?

(4,4), (4,2), (4,3), (2,4), (2,2), (2,3), (3,4), (3,2), (3,3)

What are all possible samples of size 2 without replacement?

(4,2), (4,3), (2,4), (2,3), (3,4), (3,2)

How many samples are there with replacement?

9

How many samples are there without replacement?

6

What is the population mean and standard deviation for 4K, 2K, 3K?

Mean = 3; SD ≈ 0.816

What is the mean of the sampling distribution with replacement?

3

What is the mean of the sampling distribution without replacement?

3

What is the shape of the sampling distribution if the population is normal?

Always normal, regardless of sample size

What is the shape if the population shape is unknown and the sample size is large?

Approximately normal (by Central Limit Theorem)

What is the distribution of for N(10, 1), n = 25?

0.04

What is the distribution of for mean 10, variance 4, n = 200?

0.02

P() when ?

≈ 0

P(7 < < 11)?

≈ 1

P(X < 8) if X ~ N(10, 2)?

Z = -1; P ≈ 0.1587

P(X > 11.75)?

Z = 0.875; P ≈ 0.1908

P(9.2 < X < 10.65)?

≈ 0.3108

P(X > 11 or X < 0)?

≈ 0.3085

For Binomial(100, 0.5), P(X > 10)?

≈ 1

SD of sample means for n=9 and n=36 (variance = 4)?

SDs: 0.667 and 0.333; Ratio = 2:1

State the Central Limit Theorem (CLT)

For large n, the sampling distribution of is approximately normal regardless of the population

CLT for normal population?

is always normal, any n

CLT for non-normal population?

Approximation improves as n increases

What must be assumed to compute P() for n=49?

Population is normal or n is large

What is Z for P(), ?

Z = 3.5; P ≈ 0.0002

What must be assumed to compute P() for n = 9?

Population is normal

Z-score for P() where ?

Z = -4.5; P ≈ 0

Assumption to compute P(), n = 24?

Population must be normal

Z for P(), ?

Z = -6.12; P ≈ 0

What does a normal probability plot with right skew look like?

Curve bends upward to the right

With left skew?

Curve bends downward to the left

With no skew?

Straight line

5 choose 2?

10

Mean of X if X = 1 (0.2), 2 (0.8)?

1.8

SD of X in previous?

0.16

Mean of X if values = k (0.4), 2k (0.6)?

1.6k

Variance of X in previous?

0.24k^2

Can you use normal approx. for Bin(10, 0.2)?

No

Can you use normal approx. for Bin(20, 0.4)?

Yes

Is selecting 3 students from 10 binomial?

No (not independent)

Is asking 20 residents if they're satisfied binomial?

Yes

Is asking 20 residents with 3 outcomes binomial?

No

Another name for Gaussian distribution?

Normal distribution

z0 if P(Z < z0) = 0.98?

z0 ≈ 2.05

z0 if P(-z0 < Z < z0) = 0.98?

z0 ≈ 2.33

X = 184 of 400 voters; distribution of X?

Binomial(400, 0.5)

Is it approximately normal?

Yes

Z with continuity correction for X = 184?

Z = -1.55

P(X ≤ 184)?

P(Z < -1.55) ≈ 0.0606

If n = 100, X = 46%, Z = ?

Z = -0.7; probability is higher than with n=400

If n = 1600, X = 46%, Z = ?

Z = -3.2; probability is very low

What X gives 5% probability (Z = -1.645)?

X = 183