A 2013 study by pediatricians investigates whether it is better to give children the diphtheria, tetanus and pertussis (DTaP) vaccine in the thigh or the arm. The pediatricians collected the data from two different random samples. The first random sample was collected from children who were given the vaccine in the thigh. The second random sample was collected from children who were given the vaccine in the arm. Pediatricians recorded whether the children had a severe reaction or not. No severe reaction Severe reaction Thigh Observed Expected 4758 4750.9 30 37.1 Arm Observed Expected 8840 8853.1 76 68.9 Reference: Jackson, L. A., Peterson, D., Nelson, J. C., et al. (13 co-authors). 2013. Vaccination site and risk of local reactions in children one through six years of age. Pediatrics 131: 283-289. Pediatricians conducted a chi-square test of independence. The chi-square test statistic for this data is 2.0609 with a P-value of 0.1511. What can the pediatricians conclude?

The intensity of the reaction by the application of the vaccine, do not depend on the place of the body where it is applied

Step-by-step explanation:

The chi-square test for independence between categorical variables compares the values of joint frequencies observed between the categories of the variables with the expected joint frequencies (under the hypothesis of independence between them). Thus, a high value for the test statistic means that there is a large difference between the observed and expected frequencies, while a small value for the statistic means that there is little difference between what is observed and what would be expected if the Variables were independent. A value of 2.0609 for the test statistic, with that data is small. This is confirmed with the p-value which is 0.1511 (>> 0.05) that leads to the conclusion of NOT rejecting the null hypothesis of independence between the variables.

Conclusion: The intensity of the reaction by the application of the vaccine, do not depend on the place of the body where it is applied