5. (15 points) A research professor was studying survival rates of penguins, and the professor noticed that there had been two different methods of "tagging' used. One method was "metal" - a metal tag was metal electronic attached to the penguin's foot. The second survived 35 66 method was "electronic" - a micro-chip was did not survive 132 123 imbedded under the penguin's wing. The tota 167 189 professor wanted to study how the survival rate for the "metal"-tagged penguins compared to the survival rate for the "electronic"-tagged penguin. The table summarizes information on whether or not a penguin survived, and what method of "tagging" had been used. The professor wanted to use this data to estimate the difference in the survival proportions of "metal"-tagged penguins and "electronic"-tagged penguins. Set Pm = proportion of all metal-tagged penguins who survived Pe = proportion of all elec-tagged penguins who survived a) A dotplot of a bootstrap distribution with 1000 samples for a difference between two proportions is provided. This distribution is centered at -0.163. The x-axis scale goes from -0.35 to -0.01 30 ..... 20 10 : :: :.. 8: .: .:..: 0.30 0.25 0.20 -0.15 0.10 -0.05 -0.163 This is a bootstrap distribution of the statistic (using correct notation): b) Use this graph to find a 98% confidence interval using the percentiles method. Mark the boundaries of your confidence interval on the graph, and indicate above the tails how many dots you counted. Write the interval here: c) Based on your confidence interval, is it plausible that survival rates are the same among "metal"-tagged penguins and "electronic"-tagged penguins? Justify your