A manufacturer of an automobile part has a process that is designed to produce the part with a target of 2.5 inches in length. In the past, the standard deviation of the length has been 0.035 inches. In an effort to reduce the variation in the process, the manufacturer has redesigned the process. A sample of 25 parts produced under the new process shows a sample standard deviation of 0.025 inches. Calculate the test statistic for testing whether the new process standard deviation has improved from the current process.

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Austin

Mathematics

14 September, 11:37

A manufacturer of an automobile part has a process that is designed to produce the part with a target of 2.5 inches in length. In the past, the standard deviation of the length has been 0.035 inches. In an effort to reduce the variation in the process, the manufacturer has redesigned the process. A sample of 25 parts produced under the new process shows a sample standard deviation of 0.025 inches. Calculate the test statistic for testing whether the new process standard deviation has improved from the current process.

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Kingston Irwin · Answer 1

The test statistic is - 2.

Step-by-step explanation:

Test statistic (z) = (sample sd - population sd) : sample sd/√n

sample sd = 0.025 inches

population sd = 0.035 inches

n = 25

z = (0.025 - 0.035) : 0.025/√25 = - 0.01 : 0.005 = - 2