Please answer the frq in the attached screenshots

Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. 6. Researchers are studying two different designs of computer keyboards, J and K, to investigate the effectiveness of the design on the speed of data entry. The researchers believe there is a tendency for people entering data with keyboard J to have faster entry times compared with people entering data with keyboard K. Using the same set of data for entry, the researchers randomly assigned 5 people to keyboard J and 6 people to keyboard K and recorded the number of seconds each person took to enter the data. The following dotplots show the observed entry times for the two keyboards. Keyboard J 4yrre3Pvi 160 180 200 220 240 260 280 300 Entry Time (seconds) Keyboard K It'IIII''-'II 160 180 200 220 240 260 280 300 Entry Time (seconds) 17 (a) Explain why it is not appropriate to conduct a two-sample t-test for the difference in population means. (13) Based on the dotplots, explain why it might be more appropriate to compare population medians instead of population means. One test used to compare population medians is the Wilcoxon Rank Sum Test. Under the assumption that the shape and variability of the distributions are the same, the test uses the rankings of the combined observed values. To conduct the test, the entry times for keyboards J and K are combined into one group and then ranked from 1 to nT , the total number of observed values in the combined group. The observed entry times, in seconds, for both keyboard types are shown in the following table. Observed Entry Times J 158 240 248 251 261 K 184 267 279 280 284 305 (c) Consider the observed entry times for keyboards J and K. (i) Complete the following table to assign ranks to the observed entry times for keyboards J and K combined. Rank 2 3 5 6 7 8 9 10 11 Keyboard J K K K Time 158 184 240 284 305 (ii) Use the completed table in (i) to calculate the sum of the ranks assigned to each keyboard. 18 Sum of ranks for J (SR]): Sum of ranks for K (SRK): The hypotheses for the Wilcoxon Rank Sum Test are as follows. Ho : The median of the distribution of entry times for all users of keyboard J and the median of the distribution of entry times for all users of keyboard K are the same. H. : The median of the distribution of entry times for all users of keyboard J is less than the median of the distribution of entry times for all users of keyboard K. The test statistic W for the test is W= SR - , where n, is the number of observations for keyboard J (d).Use the formula to calculate the test statistic W for the keyboard data.There are 462 possible assignments of 11 ranks to 5 I s and 6 Ks. If the null hypothesis is true, the 462 assignments are equally likely. The following graph shows the sampling distribution of all possible values of W resulting from the 462 assignments. Frequency :Mhomszaagggggg 2 3 4 5 6 7 8 9101112131415161'?18192021222324252627282930 W G (e) The least possible value of W in the sampling distribution is 0. (i) Find the value of SR] for W: 0. 19 (ii) Assign 5 ranks to keyboard J and 6 ranks to keyboard K so that W: 0. Show your assignments by completing the following table. "HIM (0 Use the test statistic from part(d) and the graph of the sampling distribution to decide whether there is convincing statistical evidence, at the level of a: 0.05, that the median of the distribution for all users of keyboard J is less than the median of the distribution for all users of keyboard K Support your