The piston diameter of a certain hand pump is 0.4 inch. The manager determines that the diameters are normally distributed, with a mean of 0.4 inch and a standard deviation of 0.007 inch. After recalibrating the production machine, the manager randomly selects 29 pistons and determines that the standard deviation is 0.0051 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the a=0.05 level of significance? What are the correct hypotheses for this test? The null hypothesis is Ho o The altemative hypothesis is H,: o 0.007. < 0.007. Calculate the value of the test statistic. x2= 14.863 (Round to three decimal places as needed.) Use technology to determine the P-value for the test statistic. The P-value is (Round to three decimal places as needed.)

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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The image presents a statistical hypothesis testing scenario regarding the piston diameter of a hand pump. The manager determines that the diameters are normally distributed, with a mean of 0.4 inches and a standard deviation of 0.007 inches. After recalibrating the production machine, the manager randomly selects 29 pistons and finds that the standard deviation is 0.0051 inches. The question posed is whether there is significant evidence to conclude that the standard deviation has decreased at the significance level \( \alpha = 0.05 \).

### Correct Hypotheses for the Test:
- **Null Hypothesis \( H_0 \)**: \( \sigma = 0.007 \)
- **Alternative Hypothesis \( H_a \)**: \( \sigma < 0.007 \)

### Test Statistic Calculation:
- Calculated value: \( \chi^2 = 14.863 \) (rounded to three decimal places).

### P-value Determination:
- The image prompts the user to calculate and enter the P-value (rounded to three decimal places).

No graphs or diagrams are included in the image; it consists entirely of textual information related to hypothesis testing, significance levels, and statistical calculations.
Transcribed Image Text:The image presents a statistical hypothesis testing scenario regarding the piston diameter of a hand pump. The manager determines that the diameters are normally distributed, with a mean of 0.4 inches and a standard deviation of 0.007 inches. After recalibrating the production machine, the manager randomly selects 29 pistons and finds that the standard deviation is 0.0051 inches. The question posed is whether there is significant evidence to conclude that the standard deviation has decreased at the significance level \( \alpha = 0.05 \). ### Correct Hypotheses for the Test: - **Null Hypothesis \( H_0 \)**: \( \sigma = 0.007 \) - **Alternative Hypothesis \( H_a \)**: \( \sigma < 0.007 \) ### Test Statistic Calculation: - Calculated value: \( \chi^2 = 14.863 \) (rounded to three decimal places). ### P-value Determination: - The image prompts the user to calculate and enter the P-value (rounded to three decimal places). No graphs or diagrams are included in the image; it consists entirely of textual information related to hypothesis testing, significance levels, and statistical calculations.
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