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? What are the correct hypotheses for this test?The null hypothesis is HThe alternative hypothesis is HCalculate the value of the test statisticx² (Round to three decimal places as needed.)Use technology to determine the P-value for the test statisticThe P-value is(Round to three decimal places as needed.)What is the correct conclusion at the a=0.10 level of significance?Since the P-value isthan the level of significance,the null hypothesis. Theresufficient 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.

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?

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?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

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Question

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?

What are the correct hypotheses for this test?
The null hypothesis is H
The alternative hypothesis is H
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 a=0.10 level of significance?
Since the P-value is
than the level of significance,
the null hypothesis. There
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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