Using a at .01,F (3,12), what is your critical rejection value? F (3,12) Rejection Statement: F calc = 6.37Can you reject HO?LECTURE ACTIVITY #16 Using a at .01, F ...

Determine whether you would reject or fail to reject the null hypothesis in the following situations: a. $z=1.99$, two-tailed test at $\alpha=0.05$ b. $z=0.34, z *=1.645$ c. $p=0.03, \alpha=0.05$ d. $p=0.015, \alpha=0.01$

Right. We are conducting a hypothesis test of population mean you we want to figure out it's a P value we obtained from this test lets us reject the null hypothesis. H not at significance level alpha equals 0.1 Can we use that same p value to reject? H not at the significance level alpha equals 0.5 To start off with. Let's remember that We reject H not whenever we find P value less than or equal to our significance level alpha. So if we have the P is less than 0.1 it must be the case that P is less than equal to 0.5 As a quick example, uh P is equal 2.5 That is certainly less than or equal 2.1 and accordingly is also less than equal 2.5 With this information in hand, we know that if he satisfies 0.1 that satisfies the higher significance level 0.5 and therefore the answer to this problem is yes. The p value that lets us rejected significance level 1% lets us reject h not at significance level 5%.

Right. We are conducting a hypothesis test of population mean you we want to figure out it's a P value we obtained from this test lets us reject the null hypothesis. H not at significance level alpha equals 0.1 Can we use that same p value to reject? H not at the significance level alpha equals 0.5 To start off with. Let's remember that We reject H not whenever we find P value less than or equal to our significance level alpha. So if we have the P is less than 0.1 it must be the case that P is less than equal to 0.5 As a quick example, uh P is equal 2.5 That is certainly less than or equal 2.1 and accordingly is also less than equal 2.5 With this information in hand, we know that if he satisfies 0.1 that satisfies the higher significance level 0.5 and therefore the answer to this problem is yes. The p value that lets us rejected significance level 1% lets us reject h not at significance level 5%.

And this problem we're looking for finding the rejection region um such that the probability is less than or equal to a certain number of outcomes. We're doing 20 trials and we're saying that the true probability is 200.8. So what we're going to do in order to find out what value is going to give us the rejection region of point no one is. We're gonna go to the table in the back of the book, the table that's been referred to throughout this section and we're going to look at the column under 0.8. Okay. And we're looking also at n equals 20. So we're looking at that portion of the table um Table one in appendix three. And we're gonna look down until we find where the rejection region, the probability of that is 0.1 Okay. Which in your chart is going to be at 11. Okay. So for part A the probability of it being less than or equal to 11 is 0.1 So that's at 11. Okay, So that is your answer for part A. And then for part B, we are now given, okay from our table, it's still a sample size of 20 and now we know our rejection region is at 11 and it wants us to find the beta when it is when the probability the true probability is that 0.6. So we're going to look at our table uh Table one or table one from appendix three in the back of the book and um we're still on the N equals 20. And we are going to go to the ah column 4.6 and we're gonna go down to where we're at 11 and we're gonna find that value right here. Okay. And if we're referring to that table that value at 0.6 0.44 now recall earlier that beta is the complement. Okay, because that's the probability of a type two error, not a type one error. So we are going to find the compliment of that probability in the in the table which is 0.596 So that is our probability um for part B. And then part C is gonna work out the same way. We're just changing our P value. So in its 20 we're still using the same rejection region from Part A. Which is less than or equal to 11. Um which we found a minute ago. And now our probability is 0.4. So on our vertical column we're going to go 2.4 and we're gonna look down all the way until we get to 11. We're gonna find that in our chart which is going to be 0943 again to find our beta. We are going to subtract that which gives us 0.5 0.57 which is our answer for C.

Now we have to refer to exercise 17. What was the information that we have an exercise? 17 are vested. Stick was 1.0. Okay, so our this statistic waas 1.0 and we were testing the claim. FP is greater than 0.3. We were testing the claim. If P is greater than 0.3 So this waas it right, they'll test this was the right tail test. All right. And over there we found the P value. But now we're going to use the critical value approach. So I will have to find the critical value of Z for my P value is equal to 0105 So if I use a calculator to find that my critical value for Z in this case turns out to be 1.64 critical values 1.64 And since my Z is less than 1.6 forward, this is my Z critical value. Let me write this as he start. Since this is less than this, I fail to reject Mandel hypothesis. This is my answer.