The worldwide mortality rate for the Novel Coronavirus is equal to or less than 3.4%.
Alternative Hypothesis (Ha): The worldwide mortality rate for the Novel Coronavirus is significantly higher than 3.4%.
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According to the WHO, World Health Organization, as of March 3, 2020 the estimated mortality rate for the Novel Coronavirus was 3.4%. Although the United States’ numbers are reflective of this amount at the current time, there is claim that this number is significantly higher worldwide. You are to determine the Null and Alternative Hypotheses, and determine the correct conclusion using the most impacted countries (greater than 10k cases): USA, Spain, Italy, France, Germany, UK, China, Iran, Turkey, Belgium, Netherlands, Switzerland, Canada, Brazil, Russia, Portugal, Austria, Israel, Sweden, Ireland, S. Korea, India. You will need to show all your work for all three testing types. Using the Classical method (2 standard deviations) Using the p-value method (significance level of .05) Using a 95% confidence level
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Classical Method (2 standard deviations)
To test the null hypothesis using the classical method, we can calculate the sample mean and standard deviation of the mortality rates for the most impacted countries. Let’s assume we have collected mortality rate data for each country.
Calculate the sample mean (x̄) of the mortality rates.
Calculate the sample standard deviation (s) of the mortality rates.
Calculate the z-score using the formula: z = (x̄ – μ) / (s / √n), where μ is the hypothesized mortality rate (3.4%), n is the number of countries in the sample, and x̄ and s are the sample mean and standard deviation, respectively.
Compare the calculated z-score to the critical z-value at a significance level of α (usually 0.05 or 0.01). If the calculated z-score is greater than the critical z-value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
P-value Method (significance level of 0.05)
Calculate the test statistic (t-value) using the formula: t = (x̄ – μ) / (s / √n), where x̄ is the sample mean, μ is the hypothesized mortality rate (3.4%), s is the sample standard deviation, and n is the number of countries in the sample.
Determine the degrees of freedom (df), which is equal to the sample size minus 1.
Use the t-distribution table or statistical software to find the p-value associated with the calculated t-value and degrees of freedom.
Compare the p-value to the significance level (0.05). If the p-value is less than the significance level, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
95% Confidence Level
To construct a 95% confidence interval, we can use the following steps
Calculate the sample mean (x̄) and sample standard deviation (s) of the mortality rates.
Calculate the standard error (SE) using the formula: SE = s / √n, where s is the sample standard deviation and n is the number of countries in the sample.
Determine the critical value (z-value) for a 95% confidence level. For a two-tailed test, the critical value is approximately 1.96.
Calculate the margin of error (ME) using the formula: ME = z * SE, where z is the critical value.
Construct the confidence interval using the formula: Confidence Interval = x̄ ± ME.
Conclusion
After applying the three testing methods, we can draw a conclusion about the worldwide mortality rate for the Novel Coronavirus.
Using the classical method, if the calculated z-score is greater than the critical z-value, we reject the null hypothesis. If it is smaller, we fail to reject the null hypothesis.
Using the p-value method, if the p-value is less than the significance level (0.05), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Using a 95% confidence level, if the hypothesized mortality rate of 3.4% falls within the confidence interval, we fail to reject the null hypothesis. If it does not fall within the confidence interval, we reject the null hypothesis.
Please note that I don’t have real-time data on mortality rates for the listed countries, so I cannot perform the actual
calculations or provide a conclusion based on the current data. The steps provided are a general outline of how you would perform the hypothesis testing and draw conclusions based on statistical analysis.
