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? In fact, the margin of error depends on all of the options named The observed proportion The desired level of significance The sample size The hypothesised population proportion

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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.
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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