Hypothesis test comparing the sample proportion with the population proportion
Source:    Publish Time: 2013-03-24 03:37   1664 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

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1           1        1.41             1         1.41

0          70       98.59            71       100.00

Binomial Proportion for event = 1

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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

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