Assumptions for Inference

One Sample Proportions - Conditions

1. Individuals are independent → SRS and <10% of population; 2. Sample is sufficiently large → Successes and failures ≥ 10.

Two Sample Proportions - Conditions

1. Samples are independent; 2. Data in each sample are independent → Both SRS and <10% of populations; 3. Both samples are sufficiently large → Success and failures ≥ 10 for both.

One Sample Means - df formula

df = n-1.

One Sample Means - Conditions

1. Individuals are independent → SRS and <10% of population; 2. Population has a Normal model → Histogram is unimodal and symmetric.

Matched Pairs Means - Conditions

1. Data are matched; 2. Individuals are independent → SRS and <10% of population; 3. Population of differences is Normal → Histograms of differences is unimodal and symmetric.

Two Independent Samples Means - df

df from calculator.

Two Independent Samples Means - Conditions

1. Samples are independent; 2. Data in each sample are independent → SRSs and < 10% of populations; 3. Both populations are Normal → Both histograms are unimodal and symmetric.

Chi-square Goodness of Fit - Conditions

1. Data are counts; 2. Data in sample are independent → SRS and <10% of population; 3. Sample is sufficiently large → All expected counts ≥ 5.

Chi-square Homogeneity - df formula

df = (r-1)(c-1).

Chi-square Homogeneity - Conditions

1. Data are counts; 2. Data in groups are independent → SRS and <10% of population; 3. Groups are sufficiently large → All expected counts ≥ 5.

Chi-square Independence - df formula

df = (r-1)(c-1).

Chi-square Independence - Conditions

1. Data are counts; 2. Data are independent → SRS and <10% of population; 3. Sample is sufficiently large → All expected counts ≥ 5.

Regression df formula

df = n-2.

Association in Regression - Null Hypothesis

ß = 0?

Association in Regression - Conditions

1. Form of relationship is linear → Scatterplot looks approximately linear; 2. Errors are independent → No apparent pattern in residuals plot; 3. Variability of errors is constant → Residuals plot has consistent spread; 4. Errors have a Normal model → Histogram of residuals is approximately unimodal and symmetric.