True or False: When testing a hypothesis using the Classical Approach, if the sample proportion is too many standard deviations from the proportion stated in the null hypothesis, we reject the null hypothesis.

Verified step by step guidance

1. Understand the Classical Approach to hypothesis testing: it involves comparing the test statistic to critical values determined by the significance level.
2. Identify the null hypothesis \( H_0 \) which states a specific population proportion \( p_0 \).
3. Calculate the sample proportion \( \hat{p} \) from the data.
4. Compute the test statistic (z-score) using the formula: \[ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}} \] where \( n \) is the sample size.
5. Compare the absolute value of the test statistic to the critical value(s) from the standard normal distribution. If the test statistic is too many standard deviations away (beyond the critical value), reject the null hypothesis; otherwise, do not reject it.

Key Concepts

Classical Approach to Hypothesis Testing

The Classical Approach involves comparing a test statistic to critical values derived from a theoretical distribution. If the test statistic falls into the rejection region, we reject the null hypothesis. This method relies on predetermined significance levels to decide when to reject or fail to reject the null.

Sample Proportion and Null Hypothesis Proportion

The sample proportion is the observed proportion from the data, while the null hypothesis proportion is the assumed value under the null hypothesis. Comparing these helps determine if the observed data significantly deviates from what is expected under the null.

Standard Deviations and Rejection Criteria

Standard deviations measure how far the sample proportion is from the null hypothesis proportion in standardized units. If the sample proportion is several standard deviations away, it indicates a rare event under the null, leading to rejection of the null hypothesis.