Before and after heart rate was measured from a group of participants after taking an experimental COVID19 vaccine. Which of the following conclusions is correct for the test results below. > t.test(hrdata$afterVaccine, hrdata$beforeVaccine, paired=TRUE) Paired t-test data: hrdata$afterVaccine and hrdata$beforeVaccine t = 1.4038, df = 9, p-value = 0.1939 %3D alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -2.568014 10.968014 sample estimates: mean of the differences 4.2 Hint* the first line of code should tell you the type of test you are dealing with. There is a significant difference in Heart Rate data between before and After observations. There is No difference in Heart Rate data between Before and After observations. The confidence intervals indicate that there is a difference between Before and After observations.

We are provided with the following information: Calculated t-statistic from sample values = 1.4038 Degrees of freedom, df = 9 P-value of the test = 0.1939 Level of confidence = 0.95 Level of significance, α=0.05 We will test the following hypothesis H0 : μ1=μ2 or μ1-μ2=0 (no significant difference between Heart rate data of Before and After observations), againstH0 : μ1≠μ2 We will make the decision about the hypothesis using two methods, First, rejection region method: Critical value of t-statistic (from t table) is tcrit=tα/2,df=t0.025,9=2.262 Comparing the calculated and critical value of t-statistic, t=1.4038<2.262=tcrit This implies, the calculated t-statistic does not fall in the rejection region and that due to lack of evidence, we fail to reject the null hypothesis. Hence, there is no significant difference between Heart Rate data between Before and After observations. Second, p-value approach: Compare the p-value of the test with the level of significance as follows p-value=0.1939>0.05=α Again, this implies that due to lack of evidence, we fail to reject the null hypothesis. From the given MCQs, the answer is 'There is no difference in Heart Rate data between Before and After observations'.