The medical researcher is comparing two treatments for fighting a common cold: Zinc and Vitamin C. The researcher wants to see if the patients who take Zinc have less success fighting the common cold compared to the patients taking Vitamin C. A random sample of some patients who take Zinc and others who took Vitamin C. The results of how many felt better the following day after experiencing symptoms of the common cold are shown below:**Data on Symptoms from Taking Zinc and Vitamin C for the Common Cold:**| | Zinc | Vitamin C ||------------------|------|-----------|| Less Symptoms | 342 | 553 || No Difference | 225 | 319 |**What can be concluded at the α = 0.05 level of significance?**For this study, we should use the **z-test for the difference between two population proportions**.**a. The null and alternative hypotheses would be:**\[ H_{0}: \ p_{1} \ \] [Select an answer] \[ \ p_{2} \]\[ H_{1}: \ p_{1} \ \] [Select an answer] \[ \ p_{2} \]**b. The test statistic \( z \) =**(please round your answer to 3 decimal places).**c. The p-value =**(Please round your answer to 4 decimal places).**d. The p-value is \[ ? \] α** **e. Based on this, we should [Select an answer] the null hypothesis.****f. Thus, the final conclusion is that ...**- [ ] The results are statistically significant at α = 0.05, so there is sufficient evidence to conclude that the population of all patients who took Zinc is likely to lower their symptoms of the common cold than the population of patients who took Vitamin C.- [ ] The results are statistically significant at α = 0.05, so there is sufficient evidence to conclude that the success rate for the 567 patients who take Zinc is less than the success rate for the 872 patients who took Vitamin C.- [ ] The results are statistically insignificant at α = 0.05, so there is insufficient evidence to conclude that the population of all patients who took Zinc is less likely to decrease their symptoms of the common cold than the population of patients who take Vitamin C.- [ ] The results are statistically insignificant at α = 0

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Description: The medical researcher is comparing two treatments for fighting a common cold: Zinc and Vitamin C. The researcher wants to see if the patients who take Zinc have less success fighting the common cold compared to the patients taking Vitamin C. A rand

Solution: Given information: n1=342+225=567 Sample size of zinc n2=553+319 = 872 Sample size of zinc x1=342 less symptopms of zincx2=553 less symptopms of viamin Cp1^=x1n1=342567=0.6032 Sample proportion of less symptopms of zincp2^=x2n2=553872=0.6342 Sample proportion of less symptopms of vitamin Cp^=x1+x2n1+n2=342+553567+872p^=8951439=0.6220 Pooled proportionq^=1-p^=0.3780α=0.05 Level of significance a) To test the hypothesis Ho:p1=p2 Vs Ha:p1<p2 b) Test statistic z=p1^-p2^p^×q^×(1n1+1n2)z=0.6032-0.63420.6220×0.3780×(1567+1872)z=0.6032-0.63420.235116×(0.0017636+0.0011467)z=0.6032-0.63420.235116×0.0029103z=0.6032-0.63420.0006842z=-0.0310.0261572=-1.185142z= -1.185 Test statistic z = -1.185 c) To find P value P[Z>z]=0.118009 From excel P value = 0.1180 d) The P value is grater than α=0.05 e) We should fail to reject the null hypothesis f) Conclusion : The results are statistically insignificant at α=0.05 so there is insufficient evidence to conclude that the population of all patients who took zinc is less likely to decrease their symptoms of the common cold than the population of patients who take vitamin C. Option C is correct

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he medical researcher is comparing two treatments for fighting a common cold: Zinc and Vitamin C. The esearcher wants to see if the patients who take Zinc have less success fighting the common cold compared o a patients taking vitamin C. A random sample of some patients who take Zinc and others who took itamin C. The results of how many felt better the following day after experiencing symptoms of the ommon cold: Data on Symptoms from Taking Zinc and Vitamin C for the Common Cold Vitamin Zinc Less 342 Symptoms 553 No Difference 225 319 /hat can be concluded at the a = 0.05 level of significance? For this study, we should use z-test for the difference between two population proportions a. The null and alternative hypotheses would be:

he medical researcher is comparing two treatments for fighting a common cold: Zinc and Vitamin C. The esearcher wants to see if the patients who take Zinc have less success fighting the common cold compared o a patients taking vitamin C. A random sample of some patients who take Zinc and others who took itamin C. The results of how many felt better the following day after experiencing symptoms of the ommon cold: Data on Symptoms from Taking Zinc and Vitamin C for the Common Cold Vitamin Zinc Less 342 Symptoms 553 No Difference 225 319 /hat can be concluded at the a = 0.05 level of significance? For this study, we should use z-test for the difference between two population proportions a. The null and alternative hypotheses would be:

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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