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Test the hypothesis using the P-value approach. Be sure toverify the requirements of the test.H0:p=0.4versusH1:p>0.4n=200;x=95;α=0.1Click here to view page 1 ...

Question

Test the hypothesis using the P-value approach. Be sure toverify the requirements of the test.H0:p=0.4versusH1:p>0.4n=200;x=95;α=0.1Click here to view page 1 of the table.LOADING...   Click here to view page 2 of the table.LOADING...Calculate the test statistic,z0.z0=nothing(Round to two decimal places as needed.)

Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. H0: p=0.4 versus H1: p>0.4 n=200; x=95; α=0.1 Click here to view page 1 of the table. LOADING...    Click here to view page 2 of the table. LOADING... Calculate the test statistic, z0. z0=nothing (Round to two decimal places as needed.)



Answers

Test the hypothesis using (a) the classical approach and (b) the P-value approach. Be sure to verify the requirements of the test. $$\begin{aligned} &H_{0}: p=0.6 \text { versus } H_{1}: p<0.6\\ &n=250 ; x=124 ; \alpha=0.01 \end{aligned}$$

Even the following information were asked to find a P value, associate it with the given information here and compare our P value to an Alfa 0.5 to test these hypotheses. So the first thing we need to find is a test statistic. And because we're working with proportions as given by this P bar here, we are going to compute a pool variance. So the formula for our P bar is the first sample size times the first sample proportion plus the second sample size times a second sample proportion over some of the first and second sample sizes. So in this situation that is equal to 200 times 0.22 plus 300 times 0.16 divided by 300 plus 200 and we get a test statistic of 0.184 So this is our P bar and now we can use this this value to compute a Z score. So our Z score is equal to the difference of our proportions. Divided by the square root of are pulled variants times one minus our pool variance times one over our first sample size plus one over our second sample size and all of that under a square root. So this is equal to 0.22 minus 0.16 over the square root of our P bar. We just found out to be 0.184 times one minus 10.184 one minus 10.184 times. Um, one over 200 plus one over 300 and all of that square rooted. And we get a Z test statistic of approximately 1.70 so we'll draw our normal curve. Z equals zero lies in the middle. Z equals 1.7 lives here and now we can check our oh, so part, eh? Heart lead. Um, so important. We were asked to find a p value, but we need to find the direction of, um of the hypothesis in order to discover our p value. So since this difference of means is greater than zero sorry, the difference of proportions is greater than zero. We're going to be doing a right tail t test Z test. Sorry. So we're looking at this value here, and this value represents the probability that Z is greater than or equal to 1.7, and that's hard to compute. So what we can do is find this area over here to the left of P of Z equals 1.7 and subtract that from one. So after that, we get a P value of 0.0 for four. You're a 0.44 So for a part, ay, our answer is P equals 0.44 And now we're asked to test this Against an Alfa of 0.5 Our P value is 0.440 point 044 Sorry, because 0.44 is less than our alphabet 0.5 We can reject no hypothesis. So does that mean there's sufficient evidence to support the claim that sample one has a larger proportion in the sample?

We want to conduct the hypothesis test given using a classical and be the P value approach. We have H not H a N X and alpha. Listen at the top of the document. Yeah. Step 012 in the first part of three are identical for both tests. So we compute them simultaneously and then for the latter part of step three and then for step four, the approaches differ so we divide them at the bottom the document. So first check the requirements to be able to conduct this test, we see that mp times one minus P is equal to 37 which is greater than 10. So we're allowed to use the normal distribution Steps one and 2 are already complete as I've listed here hypotheses, an alpha level are already stated. The first part of step three is to calculate the testes cystic z. We find that p hat is X over and 78 over 154.52 So, plugging that with P and N into our Z. Z equals 2.738 Now, for the classical approach, we need to find the critical value associated with our outfit equals 0.1 From AZ. Table. This is negative 1.28. Since our Z score negative .738 is not less than our critical value. We conclude that P is not in the critical region and we fail to reject the null hypothesis. Next for the P value approach as the next part of step three, we simply have to calculate the probably the Z is less than R. Z score or 30.23 So we conclude that since P is greater than alpha, we failed to reject it.

Now. This time this is a two tailed test. My Z value is minus 1.68 and my AL 50.5 So minus 1.68 this is my Z value, my Z statistic, and my Alfa is 0.5 Now, when I'm finding the p value, I will put in reserve statistic and I will choose this to be two tailed and my P value comes out to be 0.930 My P value is turning out to be 0.930 And since my P value is greater than my Alfa, I will fail to reject final hypothesis and this is going to be my answer.

We want to conduct the given hypothesis test using a a classical and be a P value approach step zero to the first part of step three are all the same for each test, so we complete them simultaneously. Then the second part of step three and step four are separate for classical and P value. Hence how we've separated amount of body this document. So to start off with we want to check the requirements to use the normal distribution for this population proportion test, N p times one minus P is 75 which is greater than 10. So it's appropriate to use the distribution. Steps one and two already complete the hypotheses and alpha are given the problem. For the first part of step three we calculate the testes, cystic C p hat is just X over N 4.24 and plugging into Z. We obtain the equals negative 0.46 Next proceeding first of the classical approach, we have to find the critical value for our alpha 0.1 from a Z table. We see that CC equals negative 1.28 which allows us to conclude P had is not in the critical reason. So do not reject a shot next for the P value message, we find the P value. That is the probability that Z is less than negative 0.46 Rz value. This gives a P value of 0.32 to eight from which we conclude P is greater than alpha. Do not reject H now.


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