AP Statistics Conditions for Inference

Question 1

One Sample T-Test (for mean)

Answer 1

1. σ is unknown
2. Individuals are independent (SRS and n < 10% of the population)
3. Population has a Normal model (histogram is unimodal and symmetric or n > 30)
4. df = n - 1

Question 2

Two Sample T-Test (for mean)

Answer 2

1. both σs are unknown
2. Two groups are independent
3. Individual data within samples are independent (SRSs and n < 10% of population)
4. Both populations are normal (both histograms are unimodal and symmetric or n > 30 for each sample)
5. df = big nasty equation that calculator uses

Question 3

Matched Pairs T-Test (for mean)

Answer 3

1. Data are matched
2. Individuals are independent (SRS and n < 10% of population)
3. Population of differences is Normal (histogram of differences is unimodal and symmetric)

Question 4

One Sample Z-Test for a Proportion

Answer 4

1. Individuals are independent (SRS and n < 10% of population)
2. Sample size is big enough (np > 10 and
   nq > 10)

Question 5

Two Sample Z-Test for Proportions

Answer 5

1. Independent groups
2. Data within each group is independent (both are SRS and n < 10% of population)
3. Both samples are large enough (number of successes and failures for both groups is at least 10)

Question 6

Regression Inference

Answer 6

1. x and y are linearly related
2. Errors are independent (residuals have consistent scatter about the regression line)
3. Variability of errors is constant (residuals plot has consistent spread)
4. Residuals are normally distributed (histogram of residuals is approximately unimodal and symmetric or Normal probability is reasonably straight)
5. Use t-test, df = n - 2

Question 7

Chi-Squared Test (Goodness-of-Fit)

Answer 7

One variable, one sample compared with population model

1. Data are counts
2. Data in sample are independent (SRS and n < 10% of population)
3. Sample is large enough (all expected counts at least 5)
4. df = # of cells - 1

Question 8

Chi-Squared Test (Homogeneity)

Answer 8

Samples from many populations compared on one variable

1. Data are counts
2. Data in sample are independent (SRS and n < 10% of population)
3. Sample is large enough (all expected counts at least 5)
4. df = (r - 1)(c - 1)

Question 9

Chi-Squared Test (Independence)

Answer 9

Sample from one population classified on 2 variables

1. Data are counts
2. Data in sample are independent (SRS and n < 10% of population)
3. Sample is large enough (all expected counts at least 5)
4. df = (r - 1)(c - 1)