Question

The piston diameter of a certain hand pump is 0.8 inch. The manager determines that the diameters are normally distributed, with a mean of 0.8 inch and a standard deviation of 0.006 inch. After recalibrating the production machine, the manager randomly selects 25 pistons and determines that the standard deviation is 0.0042 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the a=0.10 level of significance? What are the correct hypotheses for this test? The null hypothesis is H 0.006. The alternative hypothesis is H, 0 0 006. Calculate the value of the test statistic. X (Round to two decimal places as needed.) Use technology to determine the P-value for the test statistic The P-value is KRound to three decimal places as needed.). What is the correct conclusion at the a= 0.10 level of significance? Since the P-value is greater than the level of significance, do not reject the null hypothesis. There is not sufficient evidence to conclude that the standard deviation has decreased at the 0.10 level of significance

Answer 1

Horos0.006 H,:6 < 0.006 (one failed text) n=25, 5=0.0048, 2=0.10 test Stadistic. x^2 (-1) sº (25-1) (0.0049 ) 10.006)² . P-value is = 50.9825 70.10 The result is not significant ad Peolo Since, p-value is greater than the o=0:10 so, we do not reject the Ho] Conclusion ! There is not sufficient evidence to support the claim at 2=0.10 level of significance