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Question 8 (Mandatory) (6 points) Match up the following:Not reject HO when HO is falseReject HO when HO is false; or not reject HO when HO is not falseType 1 error...

Question

Question 8 (Mandatory) (6 points) Match up the following:Not reject HO when HO is falseReject HO when HO is false; or not reject HO when HO is not falseType 1 errorType 2 errorThe power of a test P(rejecting HOIHO false)Not an errorThe risk we are willing to take of a type 1 error; or the type 1 error rateReject HO when HO is true1 - 8The probability of a type 2 error

Question 8 (Mandatory) (6 points) Match up the following: Not reject HO when HO is false Reject HO when HO is false; or not reject HO when HO is not false Type 1 error Type 2 error The power of a test P(rejecting HOIHO false) Not an error The risk we are willing to take of a type 1 error; or the type 1 error rate Reject HO when HO is true 1 - 8 The probability of a type 2 error



Answers

Error probabilities You read that a statistical test at the $\alpha=0.01$ level has probability 0.14 of making a Type II error when a specific alternative is true. What is the power of the test against this alternative?

In question 17 were given that the power of the test is 0.981 and were asked to provide the probability of a Type two error. So the power of a test is one minus data. That is the probability of rejecting the no hypothesis when it is indeed false, and we're told that is zero point 981 So recall that beta is the probability off a type two air. So this is what the question is asking us to provide. So rearranging the equation, we can simply right beta equals one minus 0.981 and that equals 0.19

Reading a statistical significance at an Alfa of 0.5 has a power of 0.78 We can tell what the probabilities of a type one and type two air for this test would be. The power of a significance test against the specific alternative is the probability that the test will reject H in all when the alternative is true, Power measures the ability of the test to detect an alternative value for the parameter. So in this case, um, the probability of getting a type one error will be that Alfa of 10.5 the probability of getting a type to error. We will use the formula that the probability of a type to air is one minus the power, so one minus that power of 78 will be a 0.22

In this exercise, we're going to be considering the data on the mean Postwar card tricks of all custom workers. The null hypothesis is that the mean is equal to 72 beats per minute. And the alternative hypotheses just that Mean is greater than 72 beats per minute. We're going to be explaining what it means when we make a type one error and have two era and finally, a correct decision. No take One error occurs when we reject the null hypothesis. When it is in fact true, so it would have come if it is. In fact, it is a fact that new is equal to 72 beats per minute. However, the results of something lead to the conclusion that mu Is greater than 72 piece per minute. Now, when would we make a Type two error? We make of type two error When we fail to reject another possesses when it is in fact false. So the fact would be that mu he's greater than 72 it's per minute. However, the sampling the results of something failed to lead to that conclusion. So in other words, the sampling results is failure two support being being written on 72 beats per minute. Next we're going to uh explain what it means to make a correct decision in that in such a situation. And there are two scenarios. The first one is when in fact the mean is equal to 72 beats per minute. And the sampling results, the results of some playing do not leave the rejection of this fact. So no rejection of then I'll hypothesis failure to reject the null hypothesis. Uh Then another way of us making a correct decision Is when the fact is that the mean is greater than 72 beats per minute. And the results of sampling also lead to the same conclusion that new He's great headline, 72 beats a minute. Next we're going to be classifying the conclusion by error type. Whereas a correct decision if we reject the null hypothesis, given ah two scenarios or two fights. The first is when we know as a matter of fact that they mean Is equal to 72 beats per minute. In other words, if we know as a matter of fact that the post work hatred of casting workers equals the normal Resting heart rate of 72 beats per minute. Now, in such a situation, if we reject the null hypothesis, then we would be making a mistake because we when we reject the null hypothesis, when it is in fact true, that is a type one error. Now in the second scene part E we're going to be looking at how you would you would classify the conclusion if we rejected the narrow hypotheses, and when it was known as a matter of fact, that the heart rate of casting workers exists, the normal resting 100 observance, two beats per minute. Okay, so in other words, here say that it's a matter of fact that new Is greater than 72 beats per minute. No, if the decision was for us to reject an al hypotheses, when, In fact, they're mean is greater than 72, then we would be making the correct decision.

Let's take a look at the number of total events. It could happen because probabilities always calculated the way uh, event can happen over total number events that are possible. So let's make a table and ride out. All of the possible events has put coin one here and coin to here. The first event this possible is coin. One could land on heads coin to could land on heads. Alright, second possible event could be the first. Corn could be a tails. The second corn could be a tails. 1/3 possible event would be coined, the first corn being the heads, second coin being a tails. And then, of course, there's one more event as possible. And that's the first corn be entails. And the second coin being heads. Therefore, you can see there's actually four total advance occurring, and heads can only occur one way. There it is out of four, and so that is the reason that one out of three is incorrect. In this problem, it's one possible currents out of four. Another way you could look at is make you a tree and say that the, uh, first coin here weaken dio like this called. It's the first coin. First going could land heads or tails and then the second coin could land also heads or tails so you could branch it out like this. So what this is saying is this versus right here is heads, heads just like we have in our table. A second possibility is heads here and tails Third possibility is tails heads in. The last possibility is tales tales. So there again, you still have four total ways that it could occur. Heads could only occur both heads one time out of four. Therefore he the way you come out one out of four, not one out of three.


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