One Sample Z-Test for Proportion TEST STATISTIC
df = n-1
The test statistic for a One Sample Z-Test for Proportion is calculated using the formula:
z = (p̂ – p) / sqrt (p * (1 – p) / n)
Where:
– p̂ is the sample proportion
– p is the hypothesized population proportion (the null hypothesis)
– n is the sample size
The formula calculates the difference between the sample proportion and the hypothesized population proportion and standardizes it based on the standard error. The standard error is calculated by taking the square root of the product between the hypothesized population proportion and the complement of the proportion (1 – p) divided by the sample size.
The resulting z-score is then compared with the critical value from the standard normal distribution. If the calculated z-score is larger than the critical value, the null hypothesis is rejected and the alternative hypothesis is accepted. On the other hand, if the z-score is smaller than the critical value, the null hypothesis is not rejected.
In summary, the test statistic for a One Sample Z-Test for Proportion is used to determine whether a sample proportion is significantly different from a hypothesized population proportion, by comparing the calculated z-score with a critical value from the standard normal distribution.
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