Assumptions and Conditions for Hypothesis Testing

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One Sample (Proportion) Z Test
1. A SRS was used
2. n < 10% of the population
3. Successes and failures each >= 10
Two Sample (Proportion) Z Test
1. Data were collected independently and groups are independent
2. Data were SRSs
3. n < 10% of populations
4. Successes and failures each >= 10
One Sample (Means) t Test (df = n - 1)
1. A SRS was used
2. n < 10% of the population
3. Sample is normally distributed OR n > 30
Matched Pairs (Means) t Test (df = n - 1)
1. A SRS was used
2. n < 10% of the population
3. Differences are normally distributed OR n > 30
Two Sample (Means) t Test
1. Data were collected independently and groups are independent
2. A SRS was used
3. n < 10% of the population
4. Samples are normally distributed OR n > 30
χ2 Goodness-of-Fit Test (df = cell count - 1)
1. Data are categorical counts
2. A SRS was used
3. n < 10% of the population
4. All expected counts >= 5
χ2 Test of Homogeneity (df = (r-1)*(c-1) )
1. Data are categorical counts
2. A SRS was used
3. n < 10% of the population
4. All expected counts >= 5
χ2 Test of Independence (df = (r-1)*(c-1) )
1. Data are categorical counts
2. A SRS was used
3. n < 10% of the population
4. All expected counts >= 5
Regression Slope t Test (df = n - 2)
1. Scatterplot is approximately linear
2. No pattern in the residuals plot
3. Residuals plot has a constant spread
4. Residuals are normally distributed