**Study Context:**A professor recruited students from two large sections of an introductory health course to test the "Freshman 15" theory, which suggests that students gain 15 pounds during their first year of college. Although these students were volunteers, they were representative of the broader freshman class in terms of demographic factors including sex and ethnicity. The students were weighed at the start of the semester and then again 12 weeks later. To evaluate any significant weight change, a Wilcoxon signed-rank test will be used. The significance level is set at $ \alpha = 0.05 $.**Instructions:**- Click the provided link to access the data table of the initial and terminal weights of the students.- Another link is available for viewing the table of critical values.**Task:**a) Conduct a Wilcoxon signed-rank test to determine whether the students’ weights changed over the semester. Formulate your hypotheses, check conditions, and perform the test (with the help of technology if necessary).**Hypothesis Options:**A.- $ H_0 $: The two samples are from the same distribution.- $ H_A $: One distribution is shifted in location higher or lower than the other.B.- $ H_0 $: There is no change in the median weight over the course of the semester.- $ H_A $: The median weight changes over the course of the semester.C.- $ H_0 $: The median weight changes over the course of the semester.- $ H_A $: There is no change in the median weight over the course of the semester. ### Data Table of Freshman Weights#### Table 1: Weights of Freshman Subjects| Subject Number | Initial Weight | Terminal Weight ||----------------|----------------|-----------------|| 1 | 134 | 153 || 2 | 186 | 200 || 3 | 165 | 187 || 4 | 157 | 181 || 5 | 131 | 160 || 6 | 154 | 163 || 7 | 191 | 195 || 8 | 146 | 159 || 9 | 127 | 143 || 10 | 138 | 180 || 11 | 130 | 149 || 12 | 195 | 232 || 13 | 179 | 192 || 14 | 177 | 189 || 15 | 193 | 208 || 16 | 205 | 228 || 17 | 186 | 207 || 18 | 191 | 191 || 19 | 173 | 170 || 20 | 151 | 190 || 21 | 121 | 131 || 22 | 181 | 193 || 23 | 123 | 175 || 24 | 126 | 142 || 25 | 159 | 169 || 26 | 144 | 165 || 27 | 176 | 191 || 28 | 167 | 193 || 29 | 201 | 225 || 30 | 172 | 205 || 31 | 232 | 260 || 32 | 161 | 193 || 33 | 113 | 147 || 34 | 145 | 162 |### Critical Value TableThe critical value table lists statistical values for different levels of significance (α

This is problem based on Wilcoxon signed-rank test to compare two related samples, matched samples, or to conduct a paired difference test of repeated measurements on a single sample to assess whether their population mean ranks differ.Hypothesis:The Hypothesis areNull hypothesis H0: There is no change in the median weight over the course of the semester.Alternative hypothesis Ha: The median weight changes over the course of the semester.We use R software for the Wilcoxon signed-rank test to test the hypothesis and get outputs asTest statistic z = 2.6342P value =0.008433Decision: as p value < alpha =0.05, so reject null hypothesis. Conclusion: there is sufficient evidence to support the claim that The median weight changes over the course of the semester.R code use for this as:1x1 <- c(134,186,165,157,134,161,114,137,141,127,192,177,197,198,193,250,186,191,137,184,181,208,163,151,144,169,132,153,146,158,133,155,169,145) #Before 2x2 <- c(153,200,187,165,127,161,132,133,144,136,192,185,207,189,206,228,207,191,170,190,193,205,175,161,165,169,126,174,149,152,143,148,139,162) #After 3wilcox.test(x2, x1, alternative = "two.sided", mu = 0, paired = TRUE, exact = FALSE, correct = TRUE) 4group <- c(rep("x1", length(x1)), rep("x2", length(x2))) 5df <- data.frame(weight = c(x1, x2), group = group) 6if(!"rstatix" %in% installed.packages()){install.packages("rstatix")} 7library(rstatix) 8wilcox_effsize(df,weight ~ group, paired = TRUE)Results:a)Hypothesis areH0:There is no change in the median weight over the course of the semester.Ha: The median weight changes over the course of the semester.test statistic =2.6342P value =0.008433Conclusion:there is sufficient evidence to support the claim that The median weight changes over the course of the semester at 5% level of significance.