1. Calculate the value of the test statistic 2. Determine the P-Value for the test statistic ### Hypothesis Testing for Standard DeviationThe piston diameter of a certain hand pump is 0.7 inch. The manager determines that the diameters are normally distributed, with a mean of 0.7 inch and a standard deviation of 0.003 inch. After recalibrating the production machine, the manager randomly selects 23 pistons and determines that the standard deviation is 0.0026 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the α = 0.01 level of significance?**What are the correct hypotheses for this test?**- **The null hypothesis (H0)**: σ = 0.003- **The alternative hypothesis (H1)**: σ < 0.003**Calculate the value of the test statistic:**- **χ2 = [ ] (Round to three decimal places as needed.)**### Explanation1. **Identifying the Problem**: - We are given the standard deviation of piston diameters before and after recalibrating the production machine. - We need to test if the recalibration has significantly decreased the standard deviation using the chi-square test for variance.2. **Setting up Hypotheses**: - **Null Hypothesis (H0)**: The population standard deviation remains at 0.003. - **Alternative Hypothesis (H1)**: The population standard deviation is less than 0.003.3. **Chi-Square Test**: - Use the formula for the chi-square statistic: \[ χ^2 = \frac{(n-1)s^2}{σ^2} \] - where \( n \) is the sample size, \( s \) is the sample standard deviation, and \( σ \) is the population standard deviation under the null hypothesis.4. **Significance Level**: - The test is conducted at a 0.01 significance level (α = 0.01).5. **Calculation**: - The exact value needs to be calculated based on the given sample size (n = 23), observed sample standard deviation (0.0026), and the hypothesized population standard deviation (0.003).This section will help students understand how to perform

Name: 1. Calculate the value of the test statistic 2. Determine the P-Value
Uploaded: 2024-03-20T07:07:00.000Z
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Description: 1. Calculate the value of the test statistic 2. Determine the P-Value for the test statistic ### Hypothesis Testing for Standard DeviationThe piston diameter of a certain hand pump is 0.7 inch. The manager determines that the diameters are normally d