They both wrong on test-statistics and p-value 

Let's go through the calculation again carefully.

### **Re-calculating the Test Statistic (z-value):**

The formula for the test statistic is:

\[
z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}
\]

Given values:
- Sample mean (\(\bar{x}\)) = 58.6
- Population mean (\(\mu\)) = 65.6
- Population standard deviation (\(\sigma\)) = 19.3
- Sample size (\(n\)) = 43

### **Re-calculating the Standard Error:**

\[
\text{Standard Error} = \frac{19.3}{\sqrt{43}}
\]

### **Re-calculating the z-value:**

\[
z = \frac{58.6 - 65.6}{\text{Standard Error}}
\]

Let’s recalculate these values.The standard error is correctly calculated as approximately \(2.943\), and the z-test statistic remains \(-2.378\).

### **Re-evaluating the P-value:**
Given that the z-test statistic remains the same, let's reconsider the p-value. For a z-value of \(-2.378\) in a one-tailed test, the p-value calculation is still:

\[
p = \text{P}(Z \leq -2.378)
\]

Let's check if this is accurate.After checking, the earlier p-value calculation for a z-value of \(-2.378\) was correct, yielding approximately \(0.0087\).

### **Possible Issues:**
If the answer is incorrect based on your test's system, consider the following possibilities:
1. **Round-off Errors:** Check if the test system requires more precise rounding or specific decimal places.
2. **Interpretation Differences:** Ensure that the test statistic and p-value are input with the expected accuracy.

### **Next Steps:**
Please verify the rounding requirements or double-check the inputs. If the test requires specific rounding (e.g., three decimal places), make sure that is consistent.

Explore the calculation of test statistics and p-values in hypothesis testing scenarios. This detailed explanation covers the formulas and calculations involved, using a specific example with sample mean, population mean, standard deviation, and sample size. Suitable for advanced undergraduate students and researchers.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation