The image discusses a statistical problem related to the piston diameter of a hand pump. The diameter is normally distributed with a mean of 0.7 inches and a standard deviation of 0.005 inches. After recalibrating the production machine, the manager randomly selects 26 pistons and finds the standard deviation to be 0.0044 inches. The question posed is whether there is significant evidence to conclude that the standard deviation has decreased at the α = 0.01 level of significance.**Instructions for the Problem:**1. **Calculate the value of the test statistic:** - \(\chi^2 =\) [Box provided for entry] - (Round to three decimal places as needed.)2. **Use technology to determine the P-value for the test statistic:** - The P-value is [Box provided for entry] - (Round to three decimal places as needed.)3. **Conclusion at \(\alpha = 0.01\) level of significance:** - Since the P-value is [greater] than the level of significance, [do not reject] the null hypothesis. There [is not] sufficient evidence to conclude that the standard deviation has decreased at the 0.01 level of significance.**Additional Notes:**- Checkboxes are used for selecting the correct options related to the P-value comparison and decision on the null hypothesis.

Given that: Sample standard deviation = 0.0044 Population standard deviation = 0.005 Sample size=26

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
A coin-operated drink machine was designed to discharge a mean of 6 fluid ounces of coffee per cup. In a test of the machine, the discharge amounts in 19 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 5.92 fluid ounces and 0.24 fluid ounces, respectively. If we assume that the discharge amounts are approximately normally distributed, is there enough evidence, to conclude that the population mean discharge, μ, differs from 6 fluid ounces? Use the 0.10 level of significance. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. H₂:0 H₁ :0 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal…
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