Assumptions for Confidence Intervals and Hypothesis Testing
1 sample mean (matched pairs) Normal/Z
a. Random sample, with independent sample members.
b. Population has an approximately Normal distribution or sample size > 30.
c. Standard deviation, σ, of the population is known.
d. Sample size is < .10 of population size.
2 sample means Normal/Z
a. Random sample, with independent sample members.
b. Samples are independent
b. Populations have an approximately Normal distribution or sample sizes > 30.
c. Standard deviations, σ, of the populations are known.
d. Sample sizes are < .10 of population sizes.
1 sample mean t-distribution
a. Random sample, with independent sample members.
b. Population has an approximately Normal distribution or sample size > 30.
c. Standard deviation, σ, of the population is unknown.
d. Sample size is < .10 of population size.
2 sample means t-distribution
a. Random sample, with independent sample members.
b. Samples are independent
c. Populations have an approximately Normal distribution or sample sizes > 30.
d. Standard deviations, σ, of the populations are unknown.
e. Sample sizes are < .10 of population sizes.
1 sample proportion Normal/Z
a. Random sample, with independent sample members.
b. np or n and n(1 – p) or n(1 - ) are greater than 5.
c. Sample size is < .10 of population size.
2 sample proportions Normal/Z
a. Random sample, with independent sample members.
b. n1p1 or n1, n1(1 – p1) or n1(1 - ), n 2p2 or n2, n 2(1 – p2) or n2(1 - ) are all greater than 5.
c. Sample size is < .10 of population size.
d. Samples are independent
χ2 Goodness of Fit Test and χ2 Test for Independence
a. Random sample, with independent sample members.
b. All expected counts are > 5.
c. Sample size is < .10 of population size.
d. Data is in counts, not percentages.
Linear Regression Test (β1 = 0)
a. Random sample, with independent sample members.
bRelationship of variables is linear.
c σy (σe) are equal for all x
d the y-values (errors) are approximately normal for all x.
e The y-values are independent among all values of x.