Confidence Intervals, Hypothesis Testing, and ANOVA in COVID-19 Data Analysis

Abstract

Question 1:Confidence intervals Confidence interval refers to a range of values that one is 95% confident and certain that it contains the true mean of the sample. Variable [Name] [Name] Age 21.230794 23.1025 # of COVID Vaccines 1.6233091 2.44336 # of tests in 2022 0.3871668 1.41283 # of people in household 3.3719952 4.69467 In this context, the qualitative variable, age, has a confidence interval of 21.23 and 23.10 years. The number of COVID vaccines has a confidence interval of (1.62,2.44) while the number of tests in 2022 has a confidence interval of 0.39 and 1.41. Lastly, the number of people in a household has a confidence interval of 3.37 and 4.69. Question 2: Hypothesis The null hypothesis is that the number COVID Vaccines for Males is equal to the number of COVID Vaccines for Females while the alternative hypothesis is that the number COVID Vaccines for Males is not equal to the number of COVID Vaccines for Females. Hence, H0: μ = number of COVID Vaccines for Males is equal to the number of COVID Vaccines for Females Ha: μ ≠ Number of COVID Vaccines for Males is not equal to the number of COVID Vaccines for Females. Table 2: Hypothesis that the number of COVID Vaccines for Males is equal to the number of COVID Vaccines for Females   Male Female Mean 1.2 2.45 Variance 1.733333 0.471053 Observations 10 20 Hypothesized Mean Difference 0 df 12 t Stat -2.8171 P(T<=t) one-tail 0.007772 t Critical one-tail 1.782288 P(T<=t) two-tail 0.015543 t Critical two-tail 2.178813   A t-test which assumes unequal variances shows that the t statistic is -2.82 at 12 degrees of freedom and alpha of 0.05. We compare the t statistic with the t Critical two-tail of 2.18. The t Critical two-tail is larger than the t statistic. Therefore, we fail to reject the null hypothesis that number of COVID Vaccines for Males is equal to the number of COVID Vaccines for Females. Hence, the number of covid vaccines for the males can be considered equal to the number of COVID Vaccines for Females. Question 3: Splitting Data in to Two Groups I used the qualitative variable tested positive to split the data into two groups. I then conducted a two-sample hypothesis that the two groups are the same at alpha of 0.1 for the quantitative variable age.   NO YES Mean 22.58333 21.88889 Variance 8.810606 4.810458 Observations 12 18 Hypothesized Mean Difference 0 df 19...