1. SRS or random sample 2. n is 10% less than population 3. population is normal or large sample size (Central Limit Theorem: n ≥ 30)
TI-84 Z-Test
Ho: µ = µo 1 mean
or
( not known)
H o : Diff 0
*
or
x tn1
s n
t
2 means (matched pairs)
x o s n
1. SRS or random sample 2. n is 10% less than population 3. population is normal or large sample size (n ≥ 30) or moderate sample size with moderate skewness or outliers GRAPH DATA!! 4. For matched pairs state why they are matched.
Degrees of freedom = n - 1
TI-84 TInterval
TI-84 T-Test
Ho: µ1 = µ2
2 means (independent)
(x1 – x 2 ) t *
s12 s22 n1 n2
t
x1 – x2 s12 s22 n1 n2
Degrees of freedom = n – 1 (n = smaller sample) or use calculator
TI-84+ 2-SampTInt
TI-84+ 2-SampTTest
1. SRS or random sample 2. n is 10% less than population 3. population is normal or large sample size or moderate sample size with moderate skewness or outliers 4. independently chosen samples
Inference Formulas & Conditions Situation
Confidence Interval
Ho: p = p0
1 proportion pˆ z
ˆˆ pq n
z
TI-84+ 1-PropZInt
Two-Way Table
1. SRS or random sample 2. n is less than 10% of population 3. ST: np0 10 & nq0 10 CI: npˆ 10 & nqˆ 10
pˆ p0 p0 q0 n
1. 2. 3. 4.
Ho: p1 = p2
pˆ1 pˆ 2 z
Conditions
TI-84+ 1-PropZTest
2 proportions
More than 2 Proportions
Significance Test
pˆ1qˆ1 pˆ 2 qˆ2 n1 n2
TI-84+ 2-PropZInt
TI-84+ 2-PropZTest
Independence (1 sample, 2 variables)
Ho: All of the proportions are the same.
Homogeneity (2 samples, 2 variables)
2
O E
2
E
df = (r–1)(c–1) r = rows, c = columns
TI-84+ 2-Test
SRS or random sample population size 10n independently chosen samples ST: n1 pˆ 5 & n1qˆ 5 & n2 pˆ 5 & n2 qˆ 5 CI: n1 pˆ1 5 & n1qˆ1 5 & n2 pˆ 2 5 & n2 qˆ2 5 x1 x2 pooled for Hypothesis Test n1 n2
5.
pˆ c
1. 2. 3.
SRS or random sample independently chosen samples all expected counts are ≥ 5 and no more than 20% of expected counts are less than 5.
Inference Formulas & Conditions Situation
Confidence Interval
More than 2 Proportions
Significance Test Ho: All of the proportions are the same.
One-Way Table
2
Goodness of Fit
O E
2
Conditions 1. SRS or random sample 2. independently chosen samples 3. all expected counts are ≥ 5 and no more than 20% of expected counts are less than 5.
E
df = n – 1
b ± t*SEb
Regression Slope y x SEb
1 2 (y – yˆ ) n –2 (x – x )2
Ho: ß = 0 or H o : There is no relationship between the two variables t
1. y responses are independent1 2. true relationship is linear 3. standard deviation about the true regression line is constant 4. response varies normally
b SEb
Degrees of freedom = n - 2
TI-84+ LinRegTTest
Work to show: parameter of interest, hypotheses, verification of assumptions, name of procedure, picture, z/t/chi calculation with substituted values and results, p-value, decision, and conclusion in context.
1
Repeated observations on the same individual are not allowed.