Mathematics, 22.07.2019 16:00 Athenax
What is the probability of making a type ii error when the machine is overfilling by .5 ounces (to 4 decimals)?
Answers: 1
![\beta(\mu')=\phi\left[z_{\alpha/2}+ \frac{\mu-\mu'}{\sigma/\sqrt{n}} \right]-\phi\left[-z_{\alpha/2}+ \frac{\mu-\mu'}{\sigma/\sqrt{n}} \right]](/tpl/images/0120/1161/93ec2.png)
, also, we are given that the sample size is 30 and the population standard deviation
is  = 0.8 and α = 0.05![\beta(16.5)=\phi\left[z_{0.025}+ \frac{-0.5}{0.8/\sqrt{30}} \right]-\phi\left[-z_{0.025}+ \frac{-0.5}{0.8/\sqrt{30}} \right] \\ \\ =\phi\left[1.96+ \frac{-0.5}{0.1461} \right]-\phi\left[-1.96+ \frac{-0.5}{0.1461} \right] \\ \\ =\phi(1.96-3.4233)-\phi(-1.96-3.4233) \\ \\ =\phi(-1.4633)-\phi(-5.3833)=0.07169](/tpl/images/0120/1161/1d274.png)
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