(Solved): 25. The piston diameter of a certain hand pump is 0.6 inch. The manager determines that the dia ...

25. 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 0.003 inch. After recalibrating the production machine, the manager randomly selects 27 pistons and determines that the standard deviation is 0.0026 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the $?=0.05$ level of significance? What are the correct hypotheses for this test? The null hypothesis is ${\mathrm{H}}_0$ : (1) (2) (3) The altemative hypothesis is $H_1:$ (4) (5) (6) Calculate the value of the test statistic. $x^2=$ (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 $?=0.05$ level of significance? Since the $P$-value is ( 7 ) than the level of significance, (8) the null hypothesis. There (9) sufficient evidence to conclude that the standard deviation has decreased at the 0.05 level of significance. (1) (2) (3) 0.0026 . (4) p (5) (6) 0.0026 . (7) greater 0.003 . $?$ 0.003 . less do not reject (9) is