Complete the following problem. Ensure you show the following for each hypothesis test:
a) H0
b) H1
c) the test statistic (round to the nearest thousandth)
d) the critical value(s)
e) the P-value (round to the nearest thousandth, use 0+ if necessary)
f) the conclusion (reject H0 or fail to reject H0)
g) the final conclusion stated in non-technical terms
Suppose all requirements are met to complete each of the hypothesis tests. If a significance level is not given, think about the seriousness of a type I error to determine which level of significance to use.
1. When designing a piston to be used for a pump for transferring liquid solution, engineers specified a mean of 0.1 in. as the target for the piston radius. The maximum standard deviation is specified as 0.0005 in. The standard deviation must be small so that the manufactured pistons will function correctly in the pump. When 12 pistons are randomly selected from the production line and measured, their radii have a standard deviation of 0.00047in. In there sufficient evidence to support the claim that the pistons are being manufactured with radii that have a standard deviation less than the specified maximum of 0.0005 in.? Use a 0.05 significance level.