AP Statistics Conditions

One Sample Z-Test (for mean)

1. σ is known

2. SRS

3. normal distribution

or

n is large (>30)

Two Sample Z-Test (for mean)

1. both σs are known

2. SRS

3. independent samples

4. normal distribution

or

n is large (>30)

One Sample T-Test (for mean)

1. σ is unknown

2. SRS

3. observations have a normal distribution

or

n is large (>40)

Two Sample T-Test (for mean)

1. both σs are unknown

2. two independent SRSs

3. populations are normal

or

n1+n2 is large (>40)

One Sample Z-Test for a Proportion

1. SRS

2. population ≥10n

3. np0>10

4. n(1-p0).10

Two Sample Z-Test for Proportions

1. SRSs

2. independent samples

3. n1 p1 > 10

4. n1(1-p1)>10

5. n2 p2>10

6. n2(1-p2)>10

Regression Inference

1. x and y are linearly related

2. response variables have normal distribution at a fixed value of x

3. same σy, for all x values

Chi-Squared Test

1. SRS(s)

2. no expected counts <1

3. no more than 20% of expected counts <5

Z Confidence Interval for Mean

1. σ is known

2. SRS

3. population is normal

or

n is large (≥30)

T Confidence Interval for Mean

1. σ is unknown

2. SRS

3. population is normal

or

n is large (≥30)

T Confidence Interval for Difference of Population Proportions

1. SRS(s)

2. independent samples

3. populations are normal

or

n1+n2 is large (≥40)

Confidence Interval for Population Proportion

1. SRS

2. population ≥10n

3. n p > 10

4. n(1-p) > 19

Z Confidence Interval for Difference of Population Proportions

1. SRS(s)

2. population >10n

3. independent samples

3. n1 p1 >10

4. n1(1-p1)> 10

5. n2 p2 >10

6. n2(1-p2)> 10

Confidence Interval for Regression of Line Slopes

1.SRS

2. response variable have normal distribution at a fixed value of x

3. same σy for all x vales