Hypothesis test comparing the sample proportion with the population proportion
Source:    Publish Time: 2013-03-24 03:37   1346 Views   Size:  16px  14px  12px
Author: Xuanqian Xie Objective: To test whether the sample proportion is significantly different with the popul

Author: Xuanqian Xie


Objective: To test whether the sample proportion is significantly different with the population proportion.

Population infection rate (P0): equalling to the pooled estimates, 0.069.

Sample infection rate (% infection at a hospital, Pm): 1.4% (1/71), assuming the random independent sampling.

Null hypothesis: Pm = P0

Alternative hypothesis: Pm ≠ P0 (two sided selected, as no good reasons to select one-sided.)

 

Using exact test, I found there is no statistical significant difference between local infection rate and population infection rate.

 

 

                                Test of H0: Proportion = 0.069

 

                               Exact Test

                               One-sided Pr <=  P           0.0391

                               Two-sided = 2 * One-sided    0.0782

 

                                         Sample Size = 71

 

 

 

data bb;

input event N;

cards;

1 1

0 70

;

 

proc freq data = bb order=data;

  tables event / binomial(p=.069);

  exact binomial;

  weight N;

run;

 

 

 

                                        The FREQ Procedure

 

                                                      Cumulative    Cumulative

                    event    Frequency     Percent     Frequency      Percent

                    ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ

                        1           1        1.41             1         1.41

                        0          70       98.59            71       100.00

 

 

                                Binomial Proportion for event = 1

                               ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ

                               Proportion (P)               0.0141

                               ASE                          0.0140

                               95% Lower Conf Limit         0.0000

                               95% Upper Conf Limit         0.0415

 

                               Exact Conf Limits

                               95% Lower Conf Limit         0.0004

                               95% Upper Conf Limit         0.0760

 

                                 Test of H0: Proportion = 0.069

 

                               ASE under H0                 0.0301

                               Z                           -1.8257

                               One-sided Pr <  Z            0.0339

                               Two-sided Pr > |Z|           0.0679

 

                               Exact Test

                               One-sided Pr <=  P           0.0391

                               Two-sided = 2 * One-sided    0.0782

 

                                         Sample Size = 71