One Proportion Z Test - Formula, Example

How to Calculate One Proportion Z Test Statistics?

Formula:

z = (p^ - p0) / √p0(1 - p0) / n Where, p^ - Observed proportion, p0 - Null hypothesis value, n - sample size, Z - test statistic
Example:

A survey claims that 8 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim, a random sample of 100 doctors is obtained. Of these 95 doctors, 82 indicate that they recommend aspirin.

Given,

Observed proportion = 72 = 72 / 100 = 0.72 Sample size ( n ) = 95 Null hypothesis value ( p0 ) = 82 / 100 = 0.82

To Find,

Z Test Statistics Value,

Solution:

z = (p^ - p0) / √p0(1 - p0) / n z = (0.72 - 0.82) / √0.82(1 - 0.82) / 95 z = (-0.10) / √0.001553684 z = -0.10 / 0.039416798 z = -2.537

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