AP STAT REVIEW: Inference

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54 Terms

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Unbiased Estimator
when the center of the sampling distribution of the statistic is equal to the population parameter
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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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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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Population Distribution
distribution of responses for every individual of the population
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Sample Distribution
Distribution of responses for a single sample
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Sampling Distribution
distribution of all values for the statistic for all possible samples of a given size from a population
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Interpret Confidence Interval
“We are C% confident that the confidence interval from *to* captures the \[population parameter in context\]
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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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How to find the MoE given confidence interval
Suppose confidence interval is (A,B)

MoE = B - (Point Estimate)
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Calc function for one sample Z-test for p
\#5: 1-PropZTest
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Calc function for one sample t-test for µ
\#2: T-Test
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Degrees of Freedom (df) NOT for chi-squared
n-1
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Test statistic formula One sample t-test for µ
t=(X BAR)-µ₀ / s/√n
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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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Power of a Test
the probability a test will correctly reject the null hypothesis, given the alternate hypothesis is true
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P(Type II Error)
P(Type II error) = 1-P(Power)
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Test statistic formula for One-Sample z-test for p
z=(P HAT) - p₀ / √p₀(1-p₀)/n
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Calc function for one sample t-interval for µ
\#8: TInterval
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CI formula for one sample z-interval for p
(P HAT) ± z\* √ (P HAT) (1-P HAT)/n
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CI Formula for one sample t-interval for µ
(X BAR) ± t\* s/√n
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Calc function for one sample z-interval for p
A: 1-PropZInt
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What factors affect confidence interval width
Decreases as n increases, increases as conf level increases
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Two sample z-interval for p₁-p₂ confidence interval
2-propZInt
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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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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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Why do we check the normal/large sample condition
so the sampling distribution is approximately normal
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What does rejecting the null mean?
There is statistcial evidence to support the alternative hypothesis
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What does failing to reject the null mean
there is not convincing statistical evidence to support the alternative hypothesis
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Confidence interval for two sample t-interval for µ₁-µ₂
2-sampTInt on calc
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Type I error
when the null hypothesis is true, but is rejected
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Type II erorr
when the alternate hypothesis is true, and the null is not rejected
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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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P HAT Combined
X₁+X₂/n₁+n₂
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Test statistic for two sample z-test for p₁-p₂
2-propZTest on calc
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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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Parameter
a number that describes the population
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Statistic
number that describes the sample
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test statistic formulat-test for slope
b-β₀/SE(sub b) (df=n-2)
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Conditions for Chi-square test
Random, 10%, large counts (all expected counts ≥5)
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CI formula t-interval for slope
b±t\* SE(sub b) (df=n-2)
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test statistic formula - chi-square test for goodness of fit
x²=Σ (observed-expected)²/expected (df = #of groups -1)
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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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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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Test statistic formula chi-square test for homogeneity/independence
X²=Σ (observed-expected)²/espected (df= (rows-1)(columns-1))
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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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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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GoF Test Hypothesis
The true distribution of \[VARIABLE\] is equally proportional as \[ \] claims
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GoF Test Alt Hypothesis
The true distribution of \[VARIABLE\] is different than claimed.
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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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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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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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10% condition
n ≤ 1/10 N
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Large Counts Condition
np ≥ 10 and n(1-p) ≥ 10
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Central Limit Theorem
n≥30