Choosing the Correct Hypothesis Test

AP Statistics: Choosing the Correct Hypothesis Test

Data is Means Test Statistic is t

1 Sample?

2 Samples?

1 Sample t Test (t Test)

If Independent Use 2-Sample t Test

If paired Find differences,

use t-Test

Data is Proportions Test Statistic is z

1 Sample? 1-Prop z Test

2 Samples? 2-Prop z Test

Categorical Data Test Statistic is 2

1 Variable? 2 GOF Test

(Uses List)

Two-Way Table? 2 Test of Association

(Uses Matrix)

AP Statistics ? Hypothesis Test Statistics

Name

One-sample z-test

Formula

z= x- n

Conditions or Assumptions*

(Normal distribution or n > 30)

and known.

One-sample t-test

Paired t-test

One-proportion z-test

Two-proportion z-test

t = x - 0 sn

t = d - d0 sd n

z = lp - p0 p0 (1- p0 ) n

z=

lp1 - lp2

lp(1 -

lp)

1 n1

+

1 n2

lp = x1 + x2 n1 + n2

(Normal population or n > 30) and unknown df = n-1 (Normal population of differences or n > 30) and unknown df = n-1

n .p > 10 and n (1 - p) > 10

n1.p1 > 5 AND n1(1 - p1) > 5 and n2.p2 > 5 and n2(1 - p2) > 5 and independent observations

Two-sample t-test

Chi-Square Test

t = x1 - x2 s12 + s22 n1 n2

2 = n (Oi - Ei )2

i =1

Ei

(Normal populations or n1+n2 > 30) and independent observations and 1 and 2 unknown

All expected counts > 0 and no more than 20% are 5 or less df = n-1 for Goodness of Fit test df = (r-1)(c-1) for Test of Association

* Note that it is common to all tests that we require the sample to be an SRS

Definition of Symbols Used

n = sample size = sample mean

s = sample standard deviation 0 = population mean = population standard deviation t = t statistic df = degrees of freedom

n1 = sample 1 size n2 = sample 2 size s1 = sample 1 std. deviation s2 = sample 2 std. deviation

= sample mean of differences d0 = population mean difference sd = std. deviation of differences

p1 = proportion 1 p2 = proportion 2 1 = population 1 mean 2 = population 2 mean O = observed count E = expected count

AP Statistics ? Confidence Interval Formulas

Name

One-sample t interval

One-proportion z interval

Two-sample t interval

Formula

x ?t* s n

lp ? z * lp(1- lp) n

(x1 - x2 ) ? t *

s12 + s22 n1 n2

Conditions or Assumptions (Normal population or n > 30) and unknown df = n-1

n . lp > 10 and n (1 - lp ) > 10

(Normal populations or n1+n2 > 40) and independent observations and 1 and 2 unknown

Two-proportion z interval

(lp1 - lp2 ) ? z *

lp1(1- lp1) + lp2 (1- lp2 )

n1

n2

n1. lp 1 > 5 AND n1(1 - lp 1) > 5 and n2. lp 2 > 5 and n2(1 - lp 2) > 5 and

independent observations

* Note that it is common to all intervals that we require the sample to be an SRS

Definition of Symbols Used

n = sample size = sample mean

s = sample standard deviation = population standard deviation t* = t-statistic critical value

z* = z-statistic critical value df = degrees of freedom

1 = sample 1 mean 2 = sample 2 mean n1 = sample 1 size n2 = sample 2 size s1 = sample 1 std. deviation s2 = sample 2 std. deviation

lp = sample proportion lp 1 = sample proportion 1 lp 2 = sample proportion 2

Commonly used z* values:

C-Level 80% 90% 95% 98% 99%

z* value 1.282 1.645 1.960 2.326 2.576

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download