4 Assumptions Conditions Requirements

Assumptions / Conditions / Req. for Inference Procedures Means, with  known: z-tests and z-intervals 1-sample z-test or

1) Data gathered properly: SRS (and/or from a randomized experiment) 2) Sampling distribution of x¯ is approx. normal: -- population itself is given to be normal, OR -- n > 30, CLT says x¯ is approx normally distributed, OR -- check actual data for normality: NPP, histogram, boxplot.

confidence interval

z

2-sample z-test or confidence interval

   x  z*   n 

x 



n





1) Data gathered properly: indep SRS (and/or from a randomized experiment) 2) Sampling distribution of x¯ ‘s is approx. normal: (same as above) z

x1  x 2

 12 n1



x1  x 2   z

 22

*

12 n1



 22 n2

n2

 Means, with  UNknown: t-tests and t-intervals 

1-sample t -test or confidence interval OR matched-pairs t-test

1) Data gathered properly: SRS (and/or from a randomized experiment) 2) Sampling distribution of x¯ is approx. normal: -- population itself is given to be normal, OR -- n > 40, CLT says x¯ is approx normally distributed, OR -- n > 15, with no outliers or strong skewness, OR -- check data for normality: NPP, histogram, boxplot. -- matched pairs: all of above for the list of DIFFERENCES. 3) df = n-1

t

2-sample t-test or confidence interval 

 s  x  t *   n 

x  s n

1) Data gathered properly: indep SRS (and/or from a randomized experiment) 2) Sampling distribution ofx¯ ‘s are approx. normal (same as above) 3) df = SMALLER n -1, OR ugly number form calculator z

x1  x 2 2

x1  x 2   t

2

s1 s  2 n n2

 

*

s12 s2 2  n1 n2

Proportions: z-tests and z-intervals 1-sample z-test or confidence interval

1) Data gathered properly: SRS (and/or from a randomized experiment) 2) Sampling distrib of p^ is approx normal: -- population is at least 10 times larger than sample. -- np and n(1-p) > 10

z

2-sample z-test:



2-sample z-interval:

pˆ  po po (1 po ) n

pˆ  z*

p(1 p) n

1) Data gathered properly: indep SRS (and/or from a randomized experiment)  2) Sampling distrib of p^ ‘s is approx normal: -- population is at least 10 times larger than sample. -- for both samples, np and n(1-p) > 5 3) plain ‘p’ is the POOLED proportion of successes pˆ1  pˆ 2 z  1 1  p(1 p)   n1 n 2  1), 2), and 3) as above.



pˆ1  pˆ 2   z*

pˆ1 (1 pˆ1 ) pˆ 2 (1 pˆ 2 )  n1 n2

Chi-Square: Tests for Goodness-of-Fit and Independence 

1) Data gathered properly: SRS (and/or from a randomized experiment) 2) all expected counts at least 1 3) no more than 20% of expected counts < 5 4) for test of indep: df = (r-1)(c-1). For GOF: df = n-1 5) for test of indep, Exp count = (row total)(column total) / (table total)

Obs - Exp 

2

2  

Exp

Linear Regression: t - test and CI for slope 

1) Data gathered properly: SRS (and/or from a randomized experiment) 2) observations are independent 3) Relationship between variables is reasonably linear: PLOT IT! 4) df = number of data points – 2. 5) Use results from computer output! b b  t * SE b t SE b FIRE UP! You WILL be successful!



