A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 418 gram setting. It is believed that the machine is underfilling the bags. A 9 bag sample had a mean of 411 grams with a standard deviation of 20 . A level of significance of 0.025 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?

Answer: There is sufficient evidence to support the claim that the bags are under-filled.Step-by-step explanation:Since we have given that [tex]H_0:\mu=418\\\\H_a:\mu<418[/tex]Sample mean = 411Standard deviation = 20n = 9So, the test statistic value is given by[tex]z=\dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\\\z=\dfrac{411-418}{\dfrac{20}{\sqrt{9}}}\\\\\\z=\dfrac{-7}{\dfrac{20}{3}}\\\\\\z=-1.05[/tex]At 0.025 level of significance,critical value z = -2.306since -2.306<-1.05so, we will reject the null hypothesis.Yes, there is sufficient evidence to support the claim that the bags are underfilled.