The piston diameter of a certain hand pump is 0.6 inch. The manager determines that the diameters are normallydistributed, with a mean of 0.6 inch and a standard deviation of 0.006 inch. After re-calibrating the productionmachine, the manager randomly selects 28 pistons and determines that the standard deviation is 0.0053 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the =0.01 level ofsignificance?

a. What are the correct hypotheses for thistest?

The null hypothesis is

The alternative hypothesis is

b. 2=

(Round to three decimal places asneeded.)

Use technology to determine theP-value for the test statistic

c. Calculate the value of the test statistic.

.

TheP-value is

d. What is the correct conclusion at the =0.01 level ofsignificance?