# Hypothesis Testing and Confidence Intervals

Hypothesis Testing and Confidence Intervals

|INFERENCE PROCEDURE |CONDITIONS |TEST STATISTIC |CONFIDENCE INTERVAL |CALCULATOR |

|One Mean |SRS? | | |Stat/Test/ |

|[pic] is known |Normal? (Is n large enough? If not GRAPH!) |[pic] |[pic] |ztest or zinterval |

| |Independent? 10n < pop | | | |

|Z-test | | | | |

|Z-Interval | | | | |

|One Mean |SRS? | | |Stats/Test/ |

|[pic] is UNKNOWN |Normal? (Is n large enough? If not GRAPH!) |[pic] |[pic] |ttest or tinterval |

| |Independent? 10n < pop |df = n-1 |df = n-1 | |

|t-test | | | | |

|t-interval | | | | |

|One Proportion |SRS? | | |Stat/Test |

| |Normal? |[pic] |[pic] |1propzTest or |

|1 Proportion z-test |np > 10, n(1-p) > 10 | | |1propZInt |

|1 Proportion z-int |Independent? 10n < pop | | | |

|More than 1 prop |SRS? | |N/A |For GOF: Put observed counts in L1 |

|2 Categorical Variables |All expected counts [pic]5? |[pic] | |and expected counts in L2. [pic] |

| | | | |Sum L3 to get [pic] |

|[pic]Tests: | | | |For Matrix: Put observed counts in |

|Goodness of Fit | | | |[A] Stat/Test/[pic]test |

|Homogeneity | | | | |

|Independence | | | | |

Hypothesis Testing and Confidence Intervals (cont)

|INFERENCE PROCEDURE |CONDITIONS |TEST STATISTIC |CONFIDENCE INTERVAL |CALCULATOR |

|Two Mean |SRS for both? | | |Stats/Test/ |

|[pic]’s are UNKNOWN |Normal for both? (Is n large enough? If|[pic] |[pic] |2samplettest or 2sampletint |

| |not GRAPH BOTH!) | | | |

|2 Sample t-test |Independent? If random, OK |df = smallest of [pic] and [pic] | | |

|2 Sample t-interval | |or ugly formula |df = smallest of [pic] and [pic] | |

| | | |or ugly formula | |

|Two Proportion |SRS for both? | | |Stat/Test |

| |Normal for both? |[pic] |[pic] |2propzTest or |

|2 Proportion z-test |[pic], [pic] | | |2propZInt |

|2 Proportion z-int |[pic], [pic] | | | |

| |Independent? | | | |

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

|Slope |1. All obs. independent | | |Stat/Test/ |

| |2. x and y have a linear relationship |[pic] |[pic] |linregttest |

|Linear Regression t-test |(see graph) | | | |

| |3. [pic] is same for all x (see graph)|df = n-2 | | |

| |4. y varies normally for each x | |df = n-2 | |

| |(residuals normal?) | | | |

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