Population Proportion Test

Comparing a single sample/population/group with a standard value

This method is applied when the population proportion is more appropriate measures instead of the central measures such as the mean.

Limitations on Population Proportion Testing

  1. The sample size, n must be large enough and taken from a large population

  2. Both n and p are the parameters from a binomial distribution.

  3. Both np and n(1-p) must be larger than 5.

    1. Therefore, the binomial distribution could be approximated as the normal (Gaussian) distribution.

The average unemployment rate in 2019 was observed to be 6.4% according to the Bureau of Labor Statistics (BLS). Therefore, 21,004,800 individuals were unemployed out of the total 328,200,000 population in the United States. The mean unemployment rate between 1948 and 2019 was calculated at 5.7338%. Is the current unemployment rate statistically higher than the mean unemployment in the United States?

Step 1


H0: p0=5.7338%

HA: p0>5.7338%

Step 2


Single Population Proportion Test as it matches with all criteria. MS Excel and Minitab can be used to analysis the data. The test statistics is calculated using the following formula.

Step 3


Statistical Interpretation of the Results

We reject the null hypothesis because the p-value (0) is smaller than the level of significance (α=0.05).

Step 4


The current, as of July 2019, unemployment rate has statistically increased from the historical average rate in the United States between 1948 and 1948.