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 0.005 inch. After reoalibrating the production machine, the manager randomly selects 25 pistons and determines that the standard deviation is 0.0043 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the or = 0.01 level of significance? What are the correct hypotheses for this test? The null hypothesis is H0: 0 = 0.005. The alternative hypothesis is H1: 5 10.2 (Type integers or decimals. Do not round.) Identify the test statistic. D (Round to two decimal places as needed.) Test the given claim. Assume that a simple random sample is selected from a normally distributed population. Use either the P-value method or the traditional method of A. H: 6 = 32.2 ft O B. H: 6 = 32.2 ft testing hypotheses. H1: 0> 32.2 ft H1: 6 32.2 ft OF. H: o = 32.2 ft 32.2 ft, which was the standard deviation for the old H,: 0 = 32.2 ft H1: 0# 32.2 ft production method. If it appears that the standard deviation is greater, does the new production method Find the test statistic. appear to be better or worse than the old method? Should the company take any action? x2 = 36.05 - 41, 77, -20, -75, - 45, 11, 15, 53, -9, -53, - 108, (Round to two decimal places as needed.) - 108 0 Determine the critical value(s). The critical value(s) is/are (Use a comma to separate answers as needed. Round to two decimal places as needed.)In a study of pulse rates of men, a simple random sample of 146 men results in a standard deviation of 11.1 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.01 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute; see the accompanying StatCrunch display for this test. What do the results indicate about the effectiveness of using the range rule of thumb with the "normal range" from 60 to 100 beats per minute for estimating o in this case? Assume that the simple random sample is selected from a normally distributed population. 0 Click the icon to view the StatCrunch display. Hozo = 10 H1:o 95 10 (Type integers or decimals. Do not round.) Identify the test statistic. (Round to two decimal places as needed.)