Suppose we have two thermometers. One thermometer is very precise but is delicate and heavy (X). We have another thermometer that is much cheaper and lighter, but of unknown precision (Y). We would like to know if we can (reliably) bring the lighter thermometer with us into the field. So, we set up an experiment where we expose both thermometers to 31 different temperatures and measure the temperature with each. We get the following observations x = c(O, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120) y = c(0.02, 3.99, 7.91, 12.03, 16.09, 20.00, 23.98, 28.09, 31.94, 36.03, 40.00, 44.05, 47.95, 52.00, 55.87, 59.90, 63.91, 67. 95, 72. 11, 76. 02, 80. 01, 84. 10, 88. 06, 91. 74, 96. 02, 99. 95, 103. 87, 108. 01, 111. 99, 116. 04, 120. 03) We want to decide if these thermometers seem to be measuring the same temperatures. Let' 3 use an a = Cl 06. We estimate the simple linear regression model using this data and find that 4'31 _ 0.9997883 and SEll31l= 0.0003998 We want to find a 94% Confidence Interval for 131 (Note: You can either use the reported sample statistics or you can use the raw data to answer these questions. Either will work) (a) What is the numeric value for the correct quantile for this confidence interval? S (use 4 decimals) (b) What is the margin of error (M) for this confidence interval? Z (Use 4 decimal places) (c) Based on this confidence interval, we can conclude that O The data provides evidence that the cheaper thermometer is measuring the temperature the same as the more expensive one and hence it is safe to use. 0 The data provides evidence that the cheaper thermometer isn't measuring the temperature the same as the more expensive one and hence we need to bring and use the more expensive one