Question

A recent study by the Center for Disease Control claims that a new super-contagious virus will impact a population in which it is found if left unchecked. A recent occurrence of this virus happened on an very isolated island nation with over 30,000 inhabitants. In randomly testing 400 residents of this island after the virus outbreak, a research team found 330 tested positive for having been infected by the virus.                   

1. What was the sample's proportion measure of those having been infected by the virus? That is, determine the sample measure designated as p-hat.  
2. Is the above information sufficient for you to be certain that the percentage of all in a population who contracted the virus is the same as the value computed in part a above? Why or why not?      
3. The CDC claims that this virus tends to impact over 80% of any population in which it is found and left unchecked. The research wishes to use the island nation results to test the CDC claim.   In establishing a statistical hypothesis testing of this situation, give the required null and alternative hypotheses for a test of the claim made by the CDC.         

            H0:

            H1:     

4. Based on your answer in part c, should you use a right-tailed, a left-tailed, or a two-tailed test? Briefly explain how one determines which of the three possibilities is to be used.         
5. Describe the possible Type I error for this situation--make sure to state the error in terms of the percentage of a population infected by the virus.        

                                                                       

6. Describe the possible Type II error for this situation--make sure to state make sure to state the error in terms of the percentage of a population infected by the virus.      
7. Determine the appropriate critical value(s) for this situation given a 5% significance level.           
8. Determine/calculate the value of the sample's test statistic.
9. Determine the P-value.         
10. Based upon your work above, should you "Reject the null hypothesis" or "Fail to reject the null hypothesis?" Explain why.      

K) Based upon the work above (and assuming requirements of the hypothesis tests are met), is there statistically sufficient evidence in this sample to support the claim that the percentage of a population that will be infected by the virus if left unchecked will be over 80%? Explain your reasoning.                              

Answer 1

A. From the given information, p-hat= 330/400= 0.825

B. We can use this proportion for the whole population, since we have used a sufficiently large sample of 400 to estimate this proportion.

C. We are testing,

H0: p=0.8

vs H1: p not equal 0.8

2. A. To determine what type of test to use, we look at H1. H1 above has not equal to sign, hence it's a two tailed test(if H1 had > sign then it would have been right tailed, if H1 had < sign then it would have been left tailed test)

B. A Type I error is Rejection of a true null hypothesis. Here it would be concluding that p is not equal to 0.8, when p is actually 0.8