Question

1. COVID 19 statistics as at July 28, 2020: there were 4 426 281 confirmed cases and 151 374 deaths in the United States. The worldwide mortality rate is 3.95%. You need to test if the mortality rate (proportion) in the Unites States is significantly lesser than the worldwide mortality rate.

1. Write down the null and alternative hypotheses to be tested. Clearly define the terms used.

2. What is the type of statistical test procedure that should be used to test the hypotheses? Explain.

3. Construct a 95% confidence interval. Test the hypotheses using the confidence interval. Interpret the test result clearly.

4. Test the hypotheses using the Test Statistic / Critical Value method (you must clearly indicate the test statistic, and the critical value(s) use Take α=5%). Do you get the same answer as part (c)? If your answer is the same as (c), you do not have to interpret again. Otherwise, interpret the test findings.

        

What is the P value of the test? Test the hypotheses using the P value. Take α=5%. Do you get the same answer as parts (c) and (d)? If your answer is the same as (c) and (d), you do not have to interpret again. Otherwise, interpret the test findings.

Answer 1

a) Test hypothesis are Ho: p= 3.95% H:p<3.95% b) 1 sample proportional z test will be appropriate c) Given deaths x = 15374 Sample size n= 4,426,281 Sample proportion p = x/n=0.03419891 = 0.0342 Level of confidence C =0.95 a= 0.05 Critical ze = -1.645 95% lower confidence interval is = p + z*. p(1-p) n = 0.0342 - 1.645* 0.0342(1-0.0342) 4426281 = 0.0342 -0.000142 = 0.0341 Lower one sided confidence interval for p is p>0.0341 Since hypothesized proportion is greater than confidence hence reject the null hypothesis

d) Test hypothesis are. Ho: p= 3.95% H:p<3.95% Critical value for p = 0.05 Critical value z. =2&2,3 -1.165 (Left tailed) Rejection region, Reject Ho, if z<-1.645 Test statistic z= -p P(1-p)/n 0.0342-0.0395 = -57.25813 = -57.26 0.0395(1-0.0395)/4426281 Since test statistic <-1.645 hence reject the null hypothesis Yes the both answer are same e)P-value=P(z<-57.26)=0.0000 Since p-value<0.05 hence reject the null hypothesis Yes all 3 methods given the same answer There is sufficient evidence to conclude that the mortality rate in the united states is significantly lesser than the world wide mortality rate