[Data] Observe \(y=9\) for \(n=10\) for a Binormial Y.
[Specification]
The p=0.5 conducts hypothesis testing for \(H_0:\pi=0.5\).
The WALD provides Wald CI.
The LIKELIHOODRATIO provides Likelihood Ratio CI.
The WILSON provides Score CI.
[Code and Output]
DATA OneProp;
INPUT response$ count;
DATALINEs;
"Yes" 9
"no" 1
;
PROC FREQ data=OneProp;
TABLE response/binomial (p=0.5 CL=WALD LIKELIHOODRATIO WILSON);
WEIGHT count;
run;
The FREQ Procedure
Cumulative Cumulative
response Frequency Percent Frequency Percent
-------------------------------------------------------------
"Yes" 9 90.00 9 90.00
"no" 1 10.00 10 100.00
Binomial Proportion
response = "Yes"
Proportion 0.9000
ASE 0.0949
Confidence Limits for the Binomial Proportion
Proportion = 0.9000
Type 95% Confidence Limits
Likelihood Ratio 0.6284 0.9940
Wald 0.7141 1.0000
Wilson 0.5958 0.9821
Test of H0: Proportion = 0.5
ASE under H0 0.1581
Z 2.5298
One-sided Pr > Z 0.0057
Two-sided Pr > |Z| 0.0114
Sample Size = 10