Question

A machine used to fill​ gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 125 ounces and a standard deviation of 0.30 ounces. You randomly select 40 cans and carefully measure the contents. The sample mean of the cans is 124.9 ounces. Does the machine need to be​ reset? Explain your reasoning.

Answer 1

I would say yes, reset the machine, because the sample mean of 124.9 ounces is out of the 95% confidence interval

Explanation:

It depends on your alpha level of test.

Would you be fine if the 124.9 ounces is in a 95% confidence interval?

we know u = 125 ounces, σ = 0.30 ounces

sample mean E = 124.9 ounces n = 40

Our test statistic is Z = [(E - u) / σ ]*
`√(n)` which follows a Standard Normal

so...

Check if P ( -1.96 < Z < 1.96) = 95% so

Z = [(E - u) / σ ]*
`√(n)` = [ (124.9 - 125)/ 0.3 ] *
`√(40)`

Z = (-0.1/0.3)* 6.3245 = -2.1 ... this is out of the 95% confidence interval

I would say yes, reset the machine, because the sample mean is out of the 95% confidence interval