Sampling Distribution

Question 0

A sample

Answer 0

Is a part of a population used to represent the population

Question 1

The population

Answer 1

Is the complete set of items of interest

Question 2

Population parameters

Answer 2

Population mean μ

Population standard deviation σ

Question 3

Statistics

Answer 3

Sample mean x

Sample standard deviation s

Question 4

Statistics are used to…

Answer 4

Make inferences about population parameters

Question 5

Statistics vary depending on….

Answer 5

The particular sample chosen

Question 6

The sampling distribution is unbiased if…

Answer 6

It’s mean (x) is equal to the associated population parameter (μ)

Question 7

Means are ______ measurements

Proportion are essentially ________ measurements

Answer 7

Quantitative

Qualitative

Question 8

How to find the standard deviation of a sample proportion

Answer 8

_________

s= ✔️(p(1-p))/n)

Question 9

To use normal approximation for a binomial proportion, np and n(1-p) should be at least ___

Answer 9

10

Question 10

To use normal approximation for a binomial proportion, it is important that samples are _________

Answer 10

Simple random samples

Question 11

To use normal approximation for a binomial proportion, the sample size should be no larger than…

Answer 11

10% of the population

This actually show indep, but the simple random sample requirement allows us to assume independence

Question 12

How to find the standard deviation of a sample mean (x)

Answer 12

s= _σ__

(✔️n)

Question 13

While giving the mean (x) and standard deviation (s) of a set of sample means, we do not describe….

Answer 13

The shape of the distribution

Because we can only conclude that the sample is normal if the population is normal

Question 14

No matter how the original population is distributed, if……. The set of sample means is approximately normally distributed

Answer 14

n is large enough (30)

Aka central limit theorem

Question 15

Distribution of the original population

Answer 15

May be uniform, bell-shaped, strongly skewed, etc.

Question 16

Standard deviation of two sample proportions

Answer 16

s= p1(1-p1) + p2(1-p2)

✔️ n1 n2

Question 17

The mean of the set of difference of sample proportions equals….

Answer 17

p1-p2

The difference of the population proportions

Question 18

The standard deviation of a set of differences of sample means is approximately…

Answer 18

σ1^2 + σ2^2

✔️ n1 n2

Question 19

The more either population varies from normal, the greater should be the corresponding ______

Answer 19

Sample size

*but should still be less than 10% of the population

Question 20

When to use t distributions

Answer 20

When the population standard deviation (σ) is unknown and the original pop is normally distributed

Question 21

How to find t

Answer 21

t= __x-μ__

s/(✔️n)

Question 22

t distributions are associated with…

Answer 22

Degrees of freedom (df)

df= n-1

Question 23

He last row of Table B (for t distributions) is the ______

Answer 23

Normal distribution, which is the case of the t-distribution taken when n is infinite

Question 24

Why are t distributions used so often?

Answer 24

The real world σ is almost always unknown

Question 25

The issue of sample size refined by statisticians:

The t-distribution with an SRS with large n (>40)

Answer 25

Unnecessary to make any assumptions about parent population

Question 26

The issue of sample size refined by statisticians:

The t-distribution with an SRS with medium n (15-40)

Answer 26

Sample should show no extreme values and little, if any, skewness; or assume parent population is normal

Question 27

The issue of sample size refined by statisticians:

The t-distribution with an SRS with small n (<15)

Answer 27

Sample should show no outliers and no skewness; or assume parent population is normal

Question 28

What are chi square models used for?

Answer 28

Tests (not confidence intervals)

Question 29

Chi square parameter

Answer 29

Degrees of freedom

df= n-2

Question 30

With chi square, if df is small the distribution is…

Answer 30

Skewed right

Question 31

With chi square, if df is small the distribution….

Answer 31

Becomes more symmetric and bell-shaped. (Like a t distribution)

Question 32

With chi square, for one or two df the peak occurs at ___

Answer 32

Zero

Question 33

With chi square, for 3+ df! the peak is at…

Answer 33

df-2

Question 34

Chi square distributions are _________ distributions

Answer 34

Continuous

Applying it to counting data is just an approximation

Question 35

Standard error of a proportion

Answer 35

SE(p)= pq

✔️ n

Question 36

Standard error for means

Answer 36

SE(x)= s

(✔️n)

Question 37

If the population is not normally distribution, does the sampling distribution of x have a mean equal to the population mean?

Answer 37

Yes

Question 38

The sampling distribution of p

Answer 38

The population proportion (p)

Question 39

If data from a sample is skewed left, what happens when the sample size goes from n=50 to n=200?

Answer 39

The mean stays the same
The standard deviation becomes smaller
The shape becomes closer to normal

Question 40

Why is the sample. Axiom not used as an estimator for the population maximum?

Answer 40

The sample maximum is biased

Question 41

t distributions are always ______

Answer 41

Symmetric and mound shaped

Like normal distributions