E11] .9. hospital lab has just purchased a new instrument for measuring levels of dioxin [in parts per billion]. To calibrate the new instrument, 21] samples of a "standard" water solution known to contain 45 parts per billion diosin are measured by the new instrument The observed data are given below: 44.1. 461}. 45.6. 41.3. 44.3. 4?.3. 44.5. 45.1. 42.9. 44.5 42.5. 41.5. 39.6. 42.1]. 45.3. 43.9. 45.6. 42.9. 4?.i}. 43.? For these data: 23:1?! = 338.1 and 21121 Yr: = 39.545113. a. h. Construct a QQ-plot tn check whether a [in]. or] model is reasonable for these data. Assuming a [in]. :3] model for these data. calculate a p-value to test the hypothesis H..: n = 45 and assess the amount of evidence against Ho. based on the data. _ What would you conclude here? is there evidence to suggest that adjustments should he made? Suppose the hospital lab rechecks the new instrument one week later by taking 25 new measurements on a standard solution of 45 parts per billion dioxin. Summary statistics from the new data are: y = 44.1 and s = 2.1. Based on this new information. calculate a p-value to test the hypothesis Ha: it = 45 and assess the amount or evidence against Ha, based on the data. What would you conclude about how well the instrument is working now? Is there evidence to suggest that adjustments should he made? Suppose that the manufacturer of these instruments claims that the standard deviation of the measurements is 2 parts per billion. Calculate a p-value to test the hypothesis that Ho: :3 = 2 for the original data and assess the amount of evidence against Ho. based on the data. What would you conclude about the manufacturer's claim? Now suppose that we accept the manufacturer's claim and assume we know is = 2. Use the appropriate pivotal quantity to calculate a p-value to test H:.: p = 45 for the original data with y = 44.45. assess the amount of evidence against Ha. based on the data. What would you conclude here? Is there evidence to suggest that adjustments should be mad e