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 0.004 inch. After recalibrating the production machine, the manager randomly selects 22 pistons and determines that the standard deviation is 0.0035 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the α=0.01 level of significance? What are the correct hypotheses for this test? The null hypothesis is H0: muμ sigmaσ pp less than< not equals≠ equals= greater than> 0.0035. 0.004. The alternative hypothesis is H1: sigmaσ muμ pp not equals≠ equals= greater than> less than< 0.0035. 0.004. Calculate the value of the test statistic. χ2 = Use technology to determine the P-value for the test statistic. The P-value is What is the correct conclusion at the α=0.01 level of significance? Since the P-value is greater less than the level of significance, reject do not reject the null hypothesis. There is not is sufficient evidence to conclude that the standard deviation has decreased at the 0.01 level of significance.

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ISBN:9781119256830

Author:Amos Gilat

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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 0.004 inch. After recalibrating the production machine, the manager randomly selects 22 pistons and determines that the standard deviation is 0.0035 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the

α=0.01

level of significance?

What are the correct hypotheses for this test?

The null hypothesis is

H0:

muμ

sigmaσ

less than<

not equals≠

equals=

greater than>

0.0035.

0.004.

The alternative hypothesis is

H1:

sigmaσ

muμ

not equals≠

equals=

greater than>

less than<

0.0035.

0.004.

Calculate the value of the test statistic.

χ2 =

Use technology to determine the P-value for the test statistic.

The P-value is

What is the correct conclusion at the

α=0.01

level of significance?

Since the P-value is

greater

less

than the level of significance,

reject

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.

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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