Part A
The probability of making a type ii error is equal to 1 minus the power of a hypothesis testing.
The power of a hypothesis test is given by:
![\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]](https://tex.z-dn.net/?f=%5Cbeta%28%5Cmu%27%29%3D%5Cphi%5Cleft%5Bz_%7B%5Calpha%2F2%7D%2B%20%5Cfrac%7B%5Cmu-%5Cmu%27%7D%7B%5Csigma%2F%5Csqrt%7Bn%7D%7D%20%5Cright%5D-%5Cphi%5Cleft%5B-z_%7B%5Calpha%2F2%7D%2B%20%5Cfrac%7B%5Cmu-%5Cmu%27%7D%7B%5Csigma%2F%5Csqrt%7Bn%7D%7D%20%5Cright%5D)
Given that the
machine is overfilling by .5 ounces, then

, also, we are given that the sample size is 30 and the population standard deviation
is = 0.8 and α = 0.05
Thus,
![\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](https://tex.z-dn.net/?f=%5Cbeta%2816.5%29%3D%5Cphi%5Cleft%5Bz_%7B0.025%7D%2B%20%5Cfrac%7B-0.5%7D%7B0.8%2F%5Csqrt%7B30%7D%7D%20%5Cright%5D-%5Cphi%5Cleft%5B-z_%7B0.025%7D%2B%20%5Cfrac%7B-0.5%7D%7B0.8%2F%5Csqrt%7B30%7D%7D%20%5Cright%5D%20%5C%5C%20%20%5C%5C%20%3D%5Cphi%5Cleft%5B1.96%2B%20%5Cfrac%7B-0.5%7D%7B0.1461%7D%20%5Cright%5D-%5Cphi%5Cleft%5B-1.96%2B%20%5Cfrac%7B-0.5%7D%7B0.1461%7D%20%5Cright%5D%20%5C%5C%20%20%5C%5C%20%3D%5Cphi%281.96-3.4233%29-%5Cphi%28-1.96-3.4233%29%20%5C%5C%20%20%5C%5C%20%3D%5Cphi%28-1.4633%29-%5Cphi%28-5.3833%29%3D0.07169)
Therefore, the probability of making a type II error when the machine is overfilling by .5 ounces is 1 - 0.07169 = 0.9283
Part B:
From part A, the power of the statistical test when the machine is
overfilling by .5 ounces is 0.0717.
Answer: the answer is 54
Step-by-step explanation: The error in the expression was that it was multiplied by 1 so it can't be one unless it was also 1 and it's not it is 54.
Hello!
We have two probabilities we can use; we have 170/400, for our experiment, and 1/2, which is our theoretical probability.
To solve, we just multiply the two probabilities.
=0.2125≈21.3
Therefore, we have about a 21.3% chance of this event occurring.
I hope this helps!
Answer:
Well a base with a positive exponent would be 5^3. All this means is 5x5x5 which is 125.
Step-by-step explanation:
Hope this helps!
The answer is 6.5t2+0.5t−5.5 , it’s simplified