Question

The piston diameter of a certain hand pump is 0.5 inch. The manager determines that the diameters are normally distributed, with a mean of 0.5 inch and a standard deviation of 0.006 inch. After recalibrating the production machine, the manager randomly selects 22 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 $\alpha = 0.10$ level of significance? What are the correct hypotheses for this test? The null hypothesis is $H_0: \sigma = 0.006$. The alternative hypothesis is $H_1: \sigma < 0.006$. Calculate the value of the test statistic $\chi^2 = 11.293$ (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.)

          The piston diameter of a certain hand pump is 0.5 inch. The manager determines that the diameters are normally distributed, with a mean of 0.5 inch and a standard deviation of 0.006 inch. After recalibrating the production machine, the manager randomly selects 22 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 $\alpha = 0.10$ level of significance?

What are the correct hypotheses for this test?
The null hypothesis is $H_0: \sigma = 0.006$.
The alternative hypothesis is $H_1: \sigma < 0.006$.

Calculate the value of the test statistic
$\chi^2 = 11.293$ (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.)

The piston diameter of a certain hand pump is 0.5 inch. The manager determines that the diameters are normally distributed, with a mean of 0.5 inch and a standard deviation of 0.006 inch. After recalibrating the production machine, the manager randomly selects 22 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 = 0.10 level of significance?

What are the correct hypotheses for this test?
The null hypothesis is H0: σ = 0.006.
The alternative hypothesis is H1: σ < 0.006.

Calculate the value of the test statistic
χ^2 = 11.293 (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.)

Added by Daniel M.

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