MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### Understanding the Z-Score in One-Proportion Hypothesis Tests

In the context of hypothesis testing, particularly for a one-proportion test, it is essential to understand which factors influence the z-score calculation. The z-score can be a critical value that helps determine the significance of the observed data. Let's scrutinize an example question that seeks to clarify one aspect of this concept:

**Question:**
Looking at the formula for the z-score in a one-proportion hypothesis test, which, if any, of the following does that z-score NOT depend on?
- \(\circ\) In fact, the margin of error depends on all of the options named
- \(\circ\) The observed proportion
- \(\circ\) The desired level of significance
- \(\circ\) The sample size
- \(\circ\) The hypothesised population proportion

**Explanation:**

- **The Observed Proportion:** The observed proportion is the actual proportion of the sample exhibiting a particular trait. This value directly influences the z-score calculation.
  
- **The Desired Level of Significance (\(\alpha\)):** This represents the threshold at which you reject the null hypothesis. However, note that while the significance level affects decision-making thresholds, it is not a direct component of the z-score calculation itself.
  
- **The Sample Size (\(n\)):** The sample size also plays a critical role in determining the spread and, consequently, the margin of error, which feeds into the z-score.
  
- **The Hypothesised Population Proportion (\(p_0\)):** This is the proportion of the population hypothesized under the null hypothesis and is a fundamental part of the z-score formula.

Upon analysis, the z-score itself directly depends on the observed proportion, the hypothesized population proportion, and the sample size. The desired level of significance is crucial for interpreting the z-score but does not impact its calculation.

The correct answer here is:
- \(\circ\) The desired level of significance

Remember, the significance level affects how you interpret the z-score but does not influence its value directly.
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Transcribed Image Text:### Understanding the Z-Score in One-Proportion Hypothesis Tests In the context of hypothesis testing, particularly for a one-proportion test, it is essential to understand which factors influence the z-score calculation. The z-score can be a critical value that helps determine the significance of the observed data. Let's scrutinize an example question that seeks to clarify one aspect of this concept: **Question:** Looking at the formula for the z-score in a one-proportion hypothesis test, which, if any, of the following does that z-score NOT depend on? - \(\circ\) In fact, the margin of error depends on all of the options named - \(\circ\) The observed proportion - \(\circ\) The desired level of significance - \(\circ\) The sample size - \(\circ\) The hypothesised population proportion **Explanation:** - **The Observed Proportion:** The observed proportion is the actual proportion of the sample exhibiting a particular trait. This value directly influences the z-score calculation. - **The Desired Level of Significance (\(\alpha\)):** This represents the threshold at which you reject the null hypothesis. However, note that while the significance level affects decision-making thresholds, it is not a direct component of the z-score calculation itself. - **The Sample Size (\(n\)):** The sample size also plays a critical role in determining the spread and, consequently, the margin of error, which feeds into the z-score. - **The Hypothesised Population Proportion (\(p_0\)):** This is the proportion of the population hypothesized under the null hypothesis and is a fundamental part of the z-score formula. Upon analysis, the z-score itself directly depends on the observed proportion, the hypothesized population proportion, and the sample size. The desired level of significance is crucial for interpreting the z-score but does not impact its calculation. The correct answer here is: - \(\circ\) The desired level of significance Remember, the significance level affects how you interpret the z-score but does not influence its value directly.
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