Statistical inference using R

B-type natriuretic peptide (BNP) levels give an indication of how healthy a subject's heart is (normal subjects have levels of BNP below roughly 100 pg/mL, while subjects suffering from various cardiac stressors and/or actual heart failure will have higher levels). A total of 165 subjects with similarly elevated BNP levels were randomly assigned to each of three different treatment groups, such that each group consisted of 55 subjects; one group acted as the control and received only a placebo injection, one group received an experimental drug, and one group received the standard treatment protocol. After receiving treatment, each subject's BNP levels were measured and stored for analysis.

These data are contained below. The first column contains the group identifier and the second column contains the actual measurements. Perform the appropriate statistical test using R to determine if there is a difference in BNP levels among the three different treatment groups based on the sample data in the file. Please provide your null hypothesis, the name of the statistical test being used, your R code (i.e., what you enter into R), the output generated by R, and your conclusion. DO NOT USE ANOVA (please use basic functions from R code to generate)

DATA:

Group,BNP Control,191 Control,159 Control,212 Control,147 Control,224 Control,195 Control,345 Control,288 Control,88 Control,250 Control,149 Control,211 Control,235 Control,267 Control,210 Control,312 Control,199 Control,244 Control,262 Control,230 Control,274 Control,243 Control,182 Control,126 Control,328 Control,192 Control,231 Control,256 Control,232 Control,176 Control,200 Control,219 Control,307 Control,178 Control,269 Control,242 Control,213 Control,167 Control,210 Control,221 Control,145 Control,236 Control,180 Control,220 Control,244 Control,176 Control,210 Control,245 Control,125 Control,282 Control,359 Control,278 Control,208 Control,249 Control,169 ExprmntlDrg,269 ExprmntlDrg,227 ExprmntlDrg,220 ExprmntlDrg,145 ExprmntlDrg,199 ExprmntlDrg,159 ExprmntlDrg,170 ExprmntlDrg,159 ExprmntlDrg,138 ExprmntlDrg,144 ExprmntlDrg,175 ExprmntlDrg,108 ExprmntlDrg,212 ExprmntlDrg,179 ExprmntlDrg,216 ExprmntlDrg,197 ExprmntlDrg,207 ExprmntlDrg,118 ExprmntlDrg,139 ExprmntlDrg,164 ExprmntlDrg,189 ExprmntlDrg,235 ExprmntlDrg,171 ExprmntlDrg,241 ExprmntlDrg,206 ExprmntlDrg,237 ExprmntlDrg,190 ExprmntlDrg,155 ExprmntlDrg,118 ExprmntlDrg,191 ExprmntlDrg,221 ExprmntlDrg,171 ExprmntlDrg,160 ExprmntlDrg,171 ExprmntlDrg,135 ExprmntlDrg,162 ExprmntlDrg,176 ExprmntlDrg,187 ExprmntlDrg,182 ExprmntlDrg,212 ExprmntlDrg,189 ExprmntlDrg,266 ExprmntlDrg,199 ExprmntlDrg,266 ExprmntlDrg,152 ExprmntlDrg,208 ExprmntlDrg,173 ExprmntlDrg,212 ExprmntlDrg,211 ExprmntlDrg,86 ExprmntlDrg,125 ExprmntlDrg,120 ExprmntlDrg,203 ExprmntlDrg,251 ExprmntlDrg,170 Standard,225 Standard,212 Standard,137 Standard,205 Standard,151 Standard,258 Standard,185 Standard,263 Standard,167 Standard,214 Standard,184 Standard,91 Standard,140 Standard,215 Standard,184 Standard,134 Standard,157 Standard,198 Standard,140 Standard,232 Standard,156 Standard,272 Standard,136 Standard,196 Standard,115 Standard,152 Standard,159 Standard,205 Standard,231 Standard,201 Standard,169 Standard,225 Standard,224 Standard,192 Standard,213 Standard,206 Standard,140 Standard,222 Standard,156 Standard,158 Standard,195 Standard,172 Standard,180 Standard,214 Standard,236 Standard,177 Standard,202 Standard,175 Standard,197 Standard,207 Standard,158 Standard,199 Standard,215 Standard,191 Standard,268