# Z-test: One Pop. Proportion

Instructions: This calculator conducts a Z-test for one population proportion (p). Please select the null and alternative hypotheses, type the hypothesized population proportion $$p_0$$, the significance level $$\alpha$$, the sample mean, the population standard deviation, and the sample size, and the results of the z-test for one proportion will be displayed for you:

Ho: $$p$$ $$p_0$$
Ha: $$p$$ $$p_0$$
Hypothesized Pop. Proportion ($$p_0$$)
Sample Size (N)
Number of favorable cases (X)
Significance Level ($$\alpha$$)

#### Z-Test for One Population Proportion

More about the z-test for one population proportion so you can better interpret the results obtained by this solver: A z-test for one proportion is a hypothesis test that attempts to make a claim about the population proportion (p) for a certain population attribute (proportion of males, proportion of people underage). The test has two non-overlapping hypotheses, the null and the alternative hypothesis. The null hypothesis is a statement about the population proportion, which corresponds to the assumption of no effect, and the alternative hypothesis is the complementary hypothesis to the null hypothesis. The main properties of a one sample z-test for one population proportion are:

• Depending on our knowledge about the “no effect” situation, the z-test can be two-tailed, left-tailed or right-tailed

• The main principle of hypothesis testing is that the null hypothesis is rejected if the test statistic obtained is sufficiently unlikely under the assumption that the null hypothesis is true

• The sampling distribution used to construct the test statistics is approximately normal

• The p-value is the probability of obtaining sample results as extreme or more extreme than the sample results obtained, under the assumption that the null hypothesis is true

• In a hypothesis tests there are two types of errors. Type I error occurs when we reject a true null hypothesis, and the Type II error occurs when we fail to reject a false null hypothesis

The formula for a z-statistic is

$z = \frac{\bar p – p_0 }{\sqrt{p_0(1-p_0)/n}}$

The null hypothesis is rejected when the z-statistic lies on the rejection region, which is determined by the significance level ($$\alpha$$) and the type of tail (two-tailed, left-tailed or right-tailed).

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