Download College Prep Stats Chapter 9 Important Info Sheet Section 9.2

College Prep Stats
Chapter 9 Important Info Sheet
Section 9.2
Notation: For population 1, we let:
For population 2, we let:
p1 = population proportion
n1 = size of the sample
x1 = number of successes in the sample
p2 = population proportion
n2 = size of the sample
x2 = number of successes in the sample
x1
(the sample proportion)
n1
qˆ1  1  pˆ1
x2
(the sample proportion)
n2
qˆ2  1  pˆ 2
pˆ1 
pˆ 2 
For Null and Alternative Hypotheses:
H 0 : p1  p2
H1 : p1  p2 , H1 : p1  p2 , H1 : p1  p2
Pooled estimate
x x
p 1 2
n1  n2
Test Statistic for Two Proportions
( pˆ1  pˆ 2 )
, (ZPROP Program)
z
 pq   pq 



 n1   n2 
Critical values:
*left tailed test, α is in the left tail, z* = invNorm(area in the left tail, 0, 1)
*right tailed test, α is in the right tail, z* = invNorm(area in the left tail, 0, 1)
𝛼
*two tailed test, α is divided equally between the two tails, z* = invNorm( , 0, 1)
2
P-values:
For right-tailed tests: P(z > test statistic)
*To find this probability in your calculator, type: normalcdf(z test statistic, 99999, 0, 1)
For left-tailed tests: P(z < –test statistic)
*To find this probability in your calculator, type: normalcdf(–99999, –z test statistic, 0, 1)
***Don’t forget if your test is two-sided, double your P-value***
Confidence Interval Estimate of 𝒑𝟏 − 𝒑𝟐
 ( pˆ1  pˆ 2 )  E, ( pˆ1  pˆ 2 )  E 
 pˆ qˆ   pˆ qˆ 
where E  | z* |  1 1    2 2  , (EPROP program)
 n1   n2 
MAKE SURE THAT z* IS POSITIVE WHEN YOU PLUG IT INTO YOUR CALCULATOR!!!!!!!
**Your Margin of Error should never be negative**
Section 9.3
Independent Samples with σ1 and σ2 Unknown and Not Assumed Equal
Notation For population 1, we let:
For population 2, we let:
1 = population mean
 1 = population standard deviation
2 = population mean
 2 = population standard deviation
n1 = size of the first sample
x1 = sample mean
s1 = sample standard deviation
n2 = size of the first sample
x2 = sample mean
s2 = sample standard deviation
For Null and Alternative Hypotheses:
H 0 : 1  2
H1 : 1  2 , H1 : 1  2 , H1 : 1  2
Test Statistic for Two Means: Independent Samples
t
( x1  x2 )
 s12

 n1
  s2 2 


  n2 
, (TMEAN program)
Degrees of freedom: df = n – 1 of the smaller sample
Critical values: Degrees of freedom, df = n – 1 of the smaller sample
*left tailed test, α is in the left tail, t* = invT(area in the left tail, df)
*right tailed test, α is in the right tail, t* = invT(1 – area in the right tail, df)
𝛼
*two tailed test, α is divided equally between the two tails, t* = invT( , df)
2
P-values: Degrees of freedom, df = n – 1 of the smaller sample
For right-tailed tests: P(t > test statistic)
*To find this probability in your calculator, type: tcdf(t test statistic, 99999, df)
For left-tailed tests: P(t < –test statistic)
*To find this probability in your calculator, type: tcdf(–99999, t test statistic , df)
***Don’t forget if your test is two-sided, double your P-value***
Confidence Interval Estimate of 1  2 : Independent Samples
 ( x1  x2 )  E, ( x1  x2 )  E 
s2
where E  | t* |  1
 n1
  s2 2 

 , (EMEAN Program)
  n2 
MAKE SURE THAT t* IS POSITIVE WHEN YOU PLUG IT INTO YOUR CALCULATOR!!!!!!!
**Your Margin of Error should never be negative**
Section 9.4
Notation for Dependent Samples
d = individual difference between the two values of a single matched pair
µ = mean value of the differences d for the population of paired data
d
d = mean value of the differences d for the paired sample data (equal to the mean of the x – y values)
sd = standard deviation of the differences d for the paired sample data
n = number of pairs of data.
For Null and Alternative Hypotheses:
H 0 : d  0
H1 : d  0, H1 : d  0, H1 : d  0
Hypothesis Test Statistic for Matched Pairs
t
d  d
, where degrees of freedom = n – 1
sd
n
Critical Values: Degrees of freedom (df) = n – 1.
*left tailed test, α is in the left tail, t* = invT(area in the left tail, df)
*right tailed test, α is in the right tail, t* = invT(1 – area in the right tail, df)
𝛼
*two tailed test, α is divided equally between the two tails, t* = invT( , df)
2
P-values: Degrees of freedom (df) = n – 1.
For right-tailed tests: P(t > test statistic)
*To find this probability in your calculator, type: tcdf(t test statistic, 99999, df)
For left-tailed tests: P(t < –test statistic)
*To find this probability in your calculator, type: tcdf(–99999, t test statistic , df)
***Don’t forget if your test is two-sided, double your P-value***
Confidence Intervals for Matched Pairs
 d  E, d  E 
where E  | t* |
sd
n
MAKE SURE THAT t* IS POSITIVE WHEN YOU PLUG IT INTO YOUR CALCULATOR!!!!!!!
**Your Margin of Error should never be negative**