Question

the piston diameter of a certain hand pump is 0.7 inch. the manager determines that the diameters are normally distributed, with a mean od 0.7 inch and a standard deviation of 0.003. after recalibrating the production machine the manager randomly selects 23 pistons and determines that the standard deviation is 0.0021inch.is there significant evidence for the manager to conclude that the standard deviation has decreased at the Alpha 0.10 level of significance

Answer 1

To test against

Here

sample standard deviation

and sample size

The test statistic can be written as

which under H₀ follows a chi square distribution with n -1 df.

We reject H₀ at 0.10 level of significance if

Now,

The value of the test statistic =

and critical value

Since , so we fail to reject H₀ at 0.10 level of significance and we can conclude that there is no significant evidence for the manager to conclude that the standard deviation has decreased.