Inference Guidelines - Sayre School



Inference Guidelines

Confidence Interval = estimate ± (critical value)(standard deviation of estimate) [pic]

[pic]

|Name of Test |When to Use |Hypotheses |Estimate |Parameter |Standard Deviation |P-Value |Assumptions |

| | | | | |of estimate | | |

| | | |deg. freed. | | | | |

|1 sample z-test |Does a single mean = |[pic] |[pic]the |[pic], the | |For each Alt. Hyp. |SRS from pop of interest. |

|for a mean |A hypothesized value? | |sample |hypothesized |[pic] |P(Z < z) |Sigma known |

| | | |mean |mean | |P(Z > z) |Pop approx Normal |

| | | | | | |[pic] |(draw plot to check) |

| | | | | | | | |

| | | |NA | | | | |

|1 sample t-test |Does a single mean = |[pic] |[pic]the |[pic], the | |For each Alt. Hyp. |SRS from pop of interest. |

|for a mean |A hypothesized value? | |sample |hypothesized |[pic] |P(T < t) |Pop approx Normal |

| | | |mean |mean | |P(T > t) |(draw plot to check) |

| | | | | | |[pic] |If symm, no outliers: n t) |[pic] instead of n. |

| | | |smaller n minus| | |[pic] |(draw both boxplots) |

| | | |1 | | | | |

|2 prop z test |Compare 2 proportions |[pic] | | |CI: | |Ind SRS’s |

| | | | | |[pic] |[pic] |Normal: |

| | | |[pic] |0 |Test: | |CI: [pic] |

| | | | | |[pic] | |[pic] |

| | | | | | | |Test: [pic] |

| | | | | | | |[pic] |

| | | | | | | | |

| | | |NA | | | | |

|Matched Pairs t|2 samples paired by |[pic] | | | | |Same as 1-sample |

| |some characteristic. | |[pic] | |[pic] |P(T < t) |T-test, but n refers |

| |Compare 2 groups | | |0 | |P(T > t) |To number of pairs |

| |Not independent | |pairs - 1 | | |[pic] | |

|Linear |Test for slope of |[pic] | b | |[pic] | |Lin shape in scatter |

|Regression |Reg. Line. | |slope of LSRL | | |P(T < t) |variation of y-values |

|t-test |Test for assoc of 2 | | |0 | |P(T > t) |the same (resid plot) |

| |Quant. Var. | |n - 2 | | |[pic] |resids normal |

| | | | | | | |(boxplot) |

|Name of test |When to use |Hypotheses |P-Value |Assumptions |degrees of freedom |

|Chi-Square |pop dist of props |[pic] | |SRS |# of categories minus 1 |

|Good-Fit |= hypothesized |[pic]:Null incorrect |[pic] |All exp counts at least 1 | |

| |distribution | | |no more than 20% are less than 5 | |

|Chi-Square |test assoc of |Null: No association | |SRS or entire population |(rows-1)(columns-1) |

|for ind. or |categorical variables |Alt: Association |[pic] |All exp counts at least 1 | |

|homogeneity | | | |no more than 20% are less than 5, | |

| | | | |unless 2x2-> all at least 5. | |

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