Sampling Distribution Flashcards Preview

AP Stats Exam > Sampling Distribution > Flashcards

Flashcards in Sampling Distribution Deck (42)
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0
Q

A sample

A

Is a part of a population used to represent the population

1
Q

The population

A

Is the complete set of items of interest

2
Q

Population parameters

A

Population mean μ

Population standard deviation σ

3
Q

Statistics

A

Sample mean x

Sample standard deviation s

4
Q

Statistics are used to…

A

Make inferences about population parameters

5
Q

Statistics vary depending on….

A

The particular sample chosen

6
Q

The sampling distribution is unbiased if…

A

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

7
Q

Means are ______ measurements

Proportion are essentially ________ measurements

A

Quantitative

Qualitative

8
Q

How to find the standard deviation of a sample proportion

A

_________

s= ✔️(p(1-p))/n)

9
Q

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

A

10

10
Q

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

A

Simple random samples

11
Q

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

A

10% of the population

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

12
Q

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

A

s= _σ__

(✔️n)

13
Q

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

A

The shape of the distribution

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

14
Q

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

A

n is large enough (30)

Aka central limit theorem

15
Q

Distribution of the original population

A

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

16
Q

Standard deviation of two sample proportions

A

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

✔️ n1 n2

17
Q

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

A

p1-p2

The difference of the population proportions

18
Q

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

A

σ1^2 + σ2^2

✔️ n1 n2

19
Q

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

A

Sample size

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

20
Q

When to use t distributions

A

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

21
Q

How to find t

A

t= __x-μ__

s/(✔️n)

22
Q

t distributions are associated with…

A

Degrees of freedom (df)

df= n-1

23
Q

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

A

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

24
Q

Why are t distributions used so often?

A

The real world σ is almost always unknown

25
Q

The issue of sample size refined by statisticians:

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

A

Unnecessary to make any assumptions about parent population

26
Q

The issue of sample size refined by statisticians:

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

A

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

27
Q

The issue of sample size refined by statisticians:

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

A

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

28
Q

What are chi square models used for?

A

Tests (not confidence intervals)

29
Q

Chi square parameter

A

Degrees of freedom

df= n-2

30
Q

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

A

Skewed right

31
Q

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

A

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

32
Q

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

A

Zero

33
Q

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

A

df-2

34
Q

Chi square distributions are _________ distributions

A

Continuous

Applying it to counting data is just an approximation

35
Q

Standard error of a proportion

A

SE(p)= pq

✔️ n

36
Q

Standard error for means

A

SE(x)= s

(✔️n)

37
Q

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

A

Yes

38
Q

The sampling distribution of p

A

The population proportion (p)

39
Q

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

A

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

40
Q

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

A

The sample maximum is biased

41
Q

t distributions are always ______

A

Symmetric and mound shaped

Like normal distributions