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Test the hypothesis using the P-value approach. Be sure toverify the requirements of the test. : p=0.4 versus : p>0.4n200; x100 alpha 0.1 ;...

Question

Test the hypothesis using the P-value approach. Be sure toverify the requirements of the test. : p=0.4 versus : p>0.4n200; x100 alpha 0.1 ;

Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. : p=0.4 versus : p>0.4 n200; x100 alpha 0.1 ;



Answers

Test the hypothesis using (a) the classical approach and (b) the P-value approach. Be sure to verify the requirements of the test. $$\begin{aligned} &H_{0}: p=0.55 \text { versus } H_{1}: p<0.55\\ &n=150 ; x=78 ; \alpha=0.1 \end{aligned}$$

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.

We want to conduct the hypothesis tests given here for H r h A and X and alpha. Using a the classical approach and be the P value approach. Step zero through the beginning of step three year, identical for each of these tests. And as you see the bottom of this document for the end of step three and step four we have differentiate between classical and P value. So for both tests we have to check the requirements first. Yeah, since n p times one minus P is 60 we find that this is greater than 10. So this requirements to use the normal distribution in this test are satisfied steps one and two. Already completing the problem. We have our hypotheses and confidence level. Given step three A is to calculate the testes is sexy from the formula. Given here we have P hat equals 1 24/2 50. Or extra end plugging in RP hat into the Z formula as well as our P and n give Z equals negative 3.3569 Next to the classical approach, we finally critical value. As the next step of part three, critical value for alpha equals 30.1 is -2.33. Since our Z score is less than this critical value, we conclude that Z or rather P hat is in the critical region and we reject the null hypothesis for the P value approach. The next part of step three is to find the P value for Z score. This is probably the Z is less than RZ score, which is .0004. So now we conclude ps listeners to alpha. So again we reject H9.

We want to conduct the hypothesis tests given below using a the classical approach and be the P value approach. Step zero through the first part of step three are identical for both approaches. And at the bottom of this document you see that we have differentiate the end phase of step three and step four for the classical mp value approach. So for the H and h a n X and alpha given we first check the requirements, MP Times 1 -2 is 42, which is greater than 10. So we're allowed to use normal distribution here. Ak were allowed to connect the hypothesis test. Steps one and 2 are complete. We already are given our hypotheses in our alpha level step three we want to calculate the test statistic Z equals P hat minus peanut over route peanut times one minus peanut over end. So we have P hat equals 75 over 200 or 2000.375 plugging that as well as our peanut and N into our R. Z formula of Z equals 2.3145 So first I'll give you the classical approach. We find the critical value For Alfa .05. This is using a Z. Table 1.695 Or rather 1.645 from this. We can conclude that he had it in the critical region because our Z score is greater than the critical value. So we reject H. Not next for the P value approach. The final step of part three is to find the P value for Z score. That is the probably busy is greater than Artsy score. So .0103. This time for our conclusion we appeal ethnical to alpha. So again we reject h. Not

We want to conduct the given hypothesis test using a the classical and be the pl you approach step zero. For the first part of step three are identical, so we carry them out simultaneously. Then the last five, Step three and step four for each test separate. Hence how we break it down at the bottom this document classical versus P value. So to start off with our step zero, we check the requirements to use the normal distribution mp times one minus p s 45 which is greater than 10. So it's appropriate to the normal distribution on this hypothesis test of the proportion for the population. Next steps one and two are already complete our hypotheses and alpha are given in the problem for step three. You want to calculate the check statistics, See we calculate Z by first calculating RP hot value which is X over n 4.88 in this case, plugging in gives the equals negative 1.49 To use the classical approach, we have to find the critical value associated with our alpha equals 0.5 This is critical value plus or minus 1.96 So he had is not in the critical region and we do not reject each night. We find that the P value is given for the probability that Z is greater, or rather less than our identifies east out of negative 1.49 Since it's a two tailed tests, we have to multiply that value by two, so we get 20.1362 from which we conclude peace create an alpha. Do not reject H not.


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