A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 137 ounces and a standard deviation of 0.30 ounces. You randomly select 45 cans and carefully measure the contents. The sample mean of the cans is 136.9 ounces. Does the machine need to be reset? Explain your reasoning.
Accepted Solution
A:
Answer:Step-by-step explanation:Let X be the amount of paint dispensed by a machine used to fill gallon=sized paint cans.X is Normal(137, 0.30)Sample size = 45Sample std error = 0.30/sqrt 45 =0.0447x bar = 136.9Create hypotheses as:H0: sample mean = 137Ha: sample mean not equal to 137(Two tailed test)Test statistic = (136.9-137)/0.0447=-2.237p value = 0.0257Since p >0.01, at 99% level we accept null hypothesisMachine need not be reset.