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.

Answered: Image /qna-images/answer/de5ee6fe-47cd-49ca-8a1b-0a41a89a91dd.jpg

Answered: The piston diameter of a certain hand…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The 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 25 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 a=0.10 level of significance? What are the correct hypotheses for this test? The null hypothesis is H₂: = 0.003. The alternative hypothesis is H₁: Calculate the value of the test statistic. 6 n example X = (Round to two decimal places as needed.) D 0.003. Get more help - # Clear all
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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 0.003 inch. After recalibrating the production machine, the manager randomly selects 28 pistons and determines that the standard deviation is 0.0027 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the a= 0.10 level of significance? What are the correct hypotheses for this test? The null hypothesis is H₂: 0 M The alternative hypothesis is H₁: Calculate the value of the test statistic. x² = (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.) What is the correct conclusion at the α = 0.10 level of significance? Since the P-value is than the level of significance, the null hypothesis. There C sufficient evidence to conclude that the standard…
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