AP STAT REVIEW: Inference

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Unbiased Estimator

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54 Terms

1

Unbiased Estimator

when the center of the sampling distribution of the statistic is equal to the population parameter

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2

Conditions for a 1 or 2 sample z-test or interval, one or two sample t test or t interval for mean or difference in means

Random, 10% condition, large counts

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3

Interpreting P-Value

the probability of obtaining a test statistic as extreme or more extreme than the observed test statistic when the null hypothesis is assumed to be true

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4

Population Distribution

distribution of responses for every individual of the population

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5

Sample Distribution

Distribution of responses for a single sample

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6

Sampling Distribution

distribution of all values for the statistic for all possible samples of a given size from a population

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7

Interpret Confidence Interval

“We are C% confident that the confidence interval from to captures the [population parameter in context]

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8

How to find the point estimate given confidence interval

Suppose confidence interval is (A,B)

The point estimate is the average of A and B.

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9

How to find the MoE given confidence interval

Suppose confidence interval is (A,B)

MoE = B - (Point Estimate)

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10

Calc function for one sample Z-test for p

#5: 1-PropZTest

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11

Calc function for one sample t-test for µ

#2: T-Test

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12

Degrees of Freedom (df) NOT for chi-squared

n-1

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13

Test statistic formula One sample t-test for µ

t=(X BAR)-µ₀ / s/√n

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14

Test statistic formula two-sample t-test for µ₁-µ₂

t=(X BAR₁ - X BAR₂) / √s₁²/n₁ + s₂²/n₂ OR 2-samp T-Test

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15

Power of a Test

the probability a test will correctly reject the null hypothesis, given the alternate hypothesis is true

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16

P(Type II Error)

P(Type II error) = 1-P(Power)

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17

Test statistic formula for One-Sample z-test for p

z=(P HAT) - p₀ / √p₀(1-p₀)/n

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18

Calc function for one sample t-interval for µ

#8: TInterval

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19

CI formula for one sample z-interval for p

(P HAT) ± z* √ (P HAT) (1-P HAT)/n

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20

CI Formula for one sample t-interval for µ

(X BAR) ± t* s/√n

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21

Calc function for one sample z-interval for p

A: 1-PropZInt

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22

What factors affect confidence interval width

Decreases as n increases, increases as conf level increases

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23

Two sample z-interval for p₁-p₂ confidence interval

2-propZInt

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24

Why do we check the condition for random?

So we can generalize to the population from which the sample was selected

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25

Why do we check the 10% condition

so sampling without replacement is okay, and we can use the stated formula for standard deviation

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26

Why do we check the normal/large sample condition

so the sampling distribution is approximately normal

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27

What does rejecting the null mean?

There is statistcial evidence to support the alternative hypothesis

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28

What does failing to reject the null mean

there is not convincing statistical evidence to support the alternative hypothesis

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29

Confidence interval for two sample t-interval for µ₁-µ₂

2-sampTInt on calc

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30

Type I error

when the null hypothesis is true, but is rejected

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31

Type II erorr

when the alternate hypothesis is true, and the null is not rejected

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32

How to choose the right inference procedure?

does the scenario describe mean(s), proportion(s), counts, or slope?

Does the scenario describe one sample, 2 sample, or paired data

Does the scenario describe a test or confidence interval?

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33

P HAT Combined

X₁+X₂/n₁+n₂

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34

Test statistic for two sample z-test for p₁-p₂

2-propZTest on calc

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35

Interpret the confidence level

In repeated random sampling with the same sample size, approximately C% of confidence intervals created will capture the [population parameter in context].

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36

Parameter

a number that describes the population

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37

Statistic

number that describes the sample

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38

test statistic formulat-test for slope

b-β₀/SE(sub b) (df=n-2)

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39

Conditions for Chi-square test

Random, 10%, large counts (all expected counts ≥5)

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40

CI formula t-interval for slope

b±t* SE(sub b) (df=n-2)

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41

test statistic formula - chi-square test for goodness of fit

x²=Σ (observed-expected)²/expected (df = #of groups -1)

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42

how to calculate expected counts in a chi-sguare test for homogeneity/independence

expected count = (row total)(column total) / table total

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43

Test statistic formula chi-square test for goodness of fit

X²=Σ (observed-expected)²/expected (df=number of groups-1)

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44

Test statistic formula chi-square test for homogeneity/independence

X²=Σ (observed-expected)²/espected (df= (rows-1)(columns-1))

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45

Significance test conclusion

Our P-value [p=_] is LESS/GREATER than the significance level [ALPHA = _]. Therefore we REJECT/FAIL TO REJECT the null. We DO/NOT have statistical evidence for [alternate hypothesis].

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46

How to remember how to reject null or not?

If the P-value is low, reject that hoe. If the P-value is high, the null’s that guy.

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47

GoF Test Hypothesis

The true distribution of [VARIABLE] is equally proportional as [ ] claims

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48

GoF Test Alt Hypothesis

The true distribution of [VARIABLE] is different than claimed.

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49

Chi-Squared test for homogeneity hypothesis

There is no difference in the true distribution of [VAR] for [POP 1] and [POP 2].

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50

Chi-Squared test for homogeneity alternate hypothesis

There is a difference in the true distribution of [VAR] for [POP 1] and [POP 2].

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51

Conditions for T-Test and T-Interval for slope

Truly linear (no pattern in the residual plot), Independent (10%), Normal distribution of residuals at each X (histogram of residuals is normal-ish), Equal std. dev. of resid. for all X (no heteroskedacisity), random sample

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52

10% condition

n ≤ 1/10 N

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53

Large Counts Condition

np ≥ 10 and n(1-p) ≥ 10

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54

Central Limit Theorem

n≥30

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