Mastering One Sample Z-Test For Proportion: Calculating Test Statistic And Significance

One Sample Z-Test for Proportion TEST STATISTIC

df = n-1

In a One Sample Z-Test for Proportion, the test statistic is calculated to determine the significance of the difference between a sample proportion and a hypothesized population proportion. The formula for the test statistic is as follows:

Z = (p̂ – p0) / √[(p0*(1-p0))/n]

Where:
p̂ represents the sample proportion
p0 represents the hypothesized population proportion
n represents the sample size

To compute the test statistic, we need to determine the sample proportion, the hypothesized population proportion, and the sample size. The test statistic measures how many standard errors the sample proportion is away from the hypothesized population proportion.

Once the test statistic is calculated, we can compare it to a critical value in the standard normal distribution table to determine the p-value. If the p-value is less than the level of significance (α), we reject the null hypothesis, which means that there is a significant difference between the sample proportion and the hypothesized population proportion.

In summary, the test statistic in a One Sample Z-Test for Proportion is a measure of how far the sample proportion is from the hypothesized population proportion, expressed in standard error units. It provides the basis for determining whether a sample is significantly different from what would be expected in a population with a given proportion.

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