8.20 The piston diameter of a certain hand pump is 0.6 inch. The manager determines that the diameters are normally distributed, with a mean of 0.6 inch and a standard deviation of 0.005 inch. After recalibrating the production machine, the manager randomly selects 21 pistons and determines that the standard deviation is 0.0044 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the α=0.05 level of significance? **Hypothesis Test for Standard Deviation****What are the correct hypotheses for this test?**- **The null hypothesis is \( H_0: \)** - \(_\square\) \( \sigma \leq \) - \(_\square\) \( \sigma \geq \) - \(_\square\) \( \sigma = \)- **The alternative hypothesis is \( H_1: \)** - \(_\square\) \( \sigma < \) - \(_\square\) \( \sigma > \) - \(_\square\) \( \sigma \neq \)**Calculate the value of the test statistic.**- \( \chi^2 = \_\_ \) (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 \(\alpha = 0.10\) level of significance?**- Since the P-value is \(_\square\) than the level of significance, \(_\square\) the null hypothesis. There \(_\square\) sufficient evidence to conclude that the standard deviation has decreased at the 0.10 level of significance.

The random sample of 21pistons are considered and the standard deviation is 0.0044 inch.

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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8.20 The piston diameter of a certain hand pump is 0.6 inch. The manager determines that the diameters are normally distributed, with a mean of 0.6 inch and a standard deviation of 0.005 inch. After recalibrating the production machine, the manager randomly selects 21 pistons and determines that the standard deviation is 0.0044 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the α=0.05 level of significance?

**Hypothesis Test for Standard Deviation**

**What are the correct hypotheses for this test?**

- **The null hypothesis is \( H_0: \)**
- \(_\square\) \( \sigma \leq \)
- \(_\square\) \( \sigma \geq \)
- \(_\square\) \( \sigma = \)

- **The alternative hypothesis is \( H_1: \)**
- \(_\square\) \( \sigma < \)
- \(_\square\) \( \sigma > \)
- \(_\square\) \( \sigma \neq \)

**Calculate the value of the test statistic.**

- \( \chi^2 = \_\_ \) (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 \(\alpha = 0.10\) level of significance?**

- Since the P-value is \(_\square\) than the level of significance, \(_\square\) the null hypothesis. There \(_\square\) sufficient evidence to conclude that the standard deviation has decreased at the 0.10 level of significance.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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