# Numerical Data

Statistic/Parameter Condition/Assumption How do we check?
One mean

1. Randomization Condition: Sample is a random sample (SRS) or representative of the population

2. Normality Condition: n ≥ 30 or the population distribution is fairly normal.

3. Independence Condition: The selection of each subject is independent of each other (10n < N)

1. Based on the information provided.

2. If n is small show that the sample is fairly normal.

3. Show that the inequality is true.

Two Sample Means

(Independent)

1. Randomization Condition: Sample is a random sample (SRS) or representative of the population or in experiments the treatments are randomly assigned.

2. Normality Condition: n ≥ 30 for each sample or the population distributions are normal.

3. Independence of Groups Condition: The groups are independent of each other.

1. Based on the information provided.

2. If n is small show that the sample is fairly normal with a graph.

3. Based on the information provided.

Two Sample Means

(Paired)

1. Paired Condition: The samples are dependent.

2. Randomization Condition: Sample is a random sample (SRS) or representative of the population or in experiments the treatments are randomly assigned to the subjects.

3. Normality Condition: n ≥ 30 or the population distribution is normal.

1. Based on the information provided.

2. Based on the information provided.

3. If n is small show that the distribution of the sample differences is fairly normal.

Slope of Regression Line

1. Linearity Assumption: The data seem to be a linear relationship.

2. Independent Assumption: The errors (Residuals) are independent.

3. Randomization Condition: The sample is a random sample (SRS) or representative of the population. This is necessary for generalizing.

4. Equal Variance Condition: The spread of the errors (residuals) for x value is about the same.

5. Normal Condition: The distribution of the errors is normal.

1. The scatterplot and the correlation coefficient.

2. No Pattern in the residual plot.

3. Based on the information provided.

4. Residual plot consistent. No outliers or influential data.

5. Boxplot or histogram of the residuals. Check for extreme skewedness and outliers

# Categorical Data

Statistic/Parameter Condition/Assumption How do we check?
One Proportion

1. Randomization Condition: Sample is a random sample (SRS) or representative of the population

2. Normality Condition: np≥ 10 and

nq ≥ 10.

3. Independent Condition: The selection of each subject is “independent of each other (10n < N)

1.Based on the information provided.

2. Show that the inequalities are true.

3. Show that the inequality is true.

Two Sample Proportions

(Independent)

1. Randomization Condition: Samples in each group are random samples (SRS) or representatives of their populations or in experiments the treatments are randomly assigned.

2. Normality Condition: n1p1 and n2p2 ≥ 10 and n1q1 and n2q2 ≥ 10.

3. Independent Condition: The selection of each subject is independent of each other (10n < N) for each sample. In some experiments this is not necessary.

4. Independence of Groups Condition: The groups are independent of each other.

1. Based on the information provided.

2. Show that the inequalities are true.

3. Show that the inequality is true.

4. Based on the information provided.

More than two Category Proportions

(Goodness of Fit)

1. Count Condition: The data are counts.

2. Independent Condition: Data are sampled independently

3. Large sample

1. Verify this.

2. SRS and 10n < N

3. Count > 5

More two Sample Proportions

(Test for Homogeneity)

1. Count Condition: The data are counts.

2. Independent Condition: Data in groups are independent.

3. Large sample

1. Verify this.

2. SRS and 10n < N

3. Count > 5

Relationship between Proportions of two Variables

1. Count Condition: The data are counts.

2. Independent Condition: Data are sampled independently

3. Large sample

1. Verify this.

2. SRS and 10n < N

3. Count > 5