ID

Common name

Assumptions

Comments

1:

1-sample z test for mean (or for mean difference of matched pairs)

SRS from normal population, known s .

CLT lets us relax normality assumptions for larger samples (see p.510 of textbook).

2:

1-sample t test for mean (or for mean difference of matched pairs)

SRS from normal population, unknown s .

CLT lets us relax normality assumptions for larger samples (see p.510 of textbook).

3:

2-sample z test for mean

2 independent SRS’s, rest same as for #1.

Rarely used.

4:

2-sample t test for mean

2 independent SRS’s from normal population (can relax the normality assumption for larger samples), unknown s ₁ and s ₂.

Can use n₁+n₂ instead of n to achieve the 15- or 40-item criteria on p.510. Also note that this test is especially robust when n₁ and n₂ are approx. equal. Use pooled ("equal variances") procedure only if s ₁ = s ₂ can be assumed.

5:

1-proportion z test

SRS from "large" population (at least 10n), np³ 10, n(1–p)³ 10.

Need large population so that SRS resembles sampling with replacement (i.e., "independent" trials to justify binomial model); other 2 assumptions ensure that z approximation to the binomial is reasonable. (We’re actually making 2 approximations.)

6:

2-proportion z test

2 independent SRS’s from "large" populations (at least 10n₁ and 10n₂),
n₁p₁>5, n₁(1–p₁)>5,
n₂p₂>5, n₂(1–p₂)>5.

Same comments as for #5. Note that in the usual case (H₀: p₁=p₂), standard practice is to use p=(x₁+x₂)/(n₁+n₂), the pooled estimate of sample proportion, in the "equal variances" standard deviation formula, which is shown on your AP formula sheet as Ö (p(1–p)) Ö (1/n₁ + 1/n₂).

7:

1-sample z conf. int. for m (or for mean difference of matched pairs)

Same as #1.

8:

1-sample t conf. int. for m (or for mean difference of matched pairs)

Same as #2.

9:

2-sample z conf. int. for difference of means (m ₁ – m ₂)

Same as #3.

Rarely used.

0:

2-sample t conf. int. for difference of means (m ₁ – m ₂)

Same as #4.

A:

1-proportion z conf. int. for p

Same as #5.

B:

2-proportion z conf. int. for p₁ – p₂

Same as #6, except do not use pooled estimate for p.

We avoid pooled estimate for p since we are not hypothesizing that p₁=p₂.

C:

c ² test for homogeneity of proportions, or for independence

All cells are counts from SRS, all expected counts ³ 1, avg. expected count ³ 5. For 2 ´ 2 tables, all expected counts ³ 5.

Use df = (rows–1)(cols–1). Expected counts need not be integers. TI-83 computes each expected count cell using the following formula:
cell = rowtotal · coltotal / grandtotal.

n/a

c ² goodness-of-fit test (the CHISQGOF program that we wrote in class)

All cells are counts from an SRS with all expected cells ³ 5.

Use df = (# of cells – 1). Expected counts need not be integers.

E:

linear regression t test

(1) The mean y value for each x value lies on the regression line, (2) variance about regression line does not vary with x, and (3) residuals are normally distributed about the regression line.

Use df = n – 2, where n denotes the number of data points.