Question

1. Covid 19 statistics as of July 21, 2020: there were 3 970 671 confirmed cases and 144 173 deaths in the US. The worldwide Covid 19 mortality rate is 4.15%. We need to test if the proportion of Covid 19 deaths in the US is significantly lesser than the worldwide mortality rate.   

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

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

1. c. 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.

1. d. 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

Answer:

Given,

Ho : p = 0.0415

Ha : p < 0.0415

sample proportion p^ = x/n = 144173 / 3970671 = 0.0363

test statistic = (p^ - p)/sqrt(pq/n)

substitute values

= (0.0363 - 0.0415)/sqrt(0.0415(1-0.0415)/3970671)

= - 51.95

Critical value = - 1.96

95% CI = p^ +/- z*sqrt(p^(1-p^)/n)

substitute values

= 0.0363 +/- 1.96*sqrt(0.0363(1-0.0363)/3970671)

= 0.0363 +/- 0.000184

= (0.036116 , 0.036484)

Here CI doesn't contain 0.0415, so we accept alternative.

In this, we observe that, test statistic < critical value, so we reject Ho.

P value = P(t < - 51.95)

= 0

Here p value < alpha, so we reject Ho.

So there is sufficient evidence to support the claim.