A certain type of stainless steel powder is supposed to have

Solution

Let mu be the population mean

The test hypothesis:

Ho: mu=15 (i.e. null hypothesis)

Ha: mu not equal to 15 (i.e. alternative hypothesis)

The test statistic is

Z=(xbar-mu)/(s/vn)

=(15.2-15)/(1.8/sqrt(87))

=1.04

It is a two-tailed test.

So the p-value= 2*P(Z>1.04) =0.2983 (from standard normal table)

Since the p-value is larger than 0.05, we do not reject the null hypothesis.

So we can conclude that A certain type of stainless steel powder is supposed to have a mean particle diameter of 15