Chapter 12, Problem 77SE

Open water oil spills can wreak terrible consequences on the environment and be expensive to clean up. Many physical and biological methods have been developed to recover oil from water surfaces. The article “Capacity of Straw for Repeated Binding of Crude Oil from Salt Water and Its Effect on Biodegradation” (J. of Hazardous Toxic and Radioactive Waste, 2012: 75–78) discussed how wheat straw could be used to extract crude oil from a water surface. An experiment was conducted in which crude oil (0 to 16.9g) was added to 100mL of saltwater in separate Petri dishes. Wheat straw (2g) was then added to each dish and all dishes were shaken at 70 rpm overnight. The following data, read from a graph, is based on the x = amount of oil added (in g) and y = the corresponding amount of oil recovered (in g) from wheat straw.

x	1.0	1.5	2.1	2.8	3.6	4.5	5.5
y	0.610	0.840	1.512	1.792	2.952	2.880	4.400

x	6.6	7.8	9.1	10.5	12.0	13.6	15.2	16.9
y	5.346	6.396	7.189	8.085	9.840	11.696	13.224	14.365

1. a. Construct a scatterplot of the data. Does it appear that recovered oil could be very well predicted by the value of added oil? Explain your reasoning.
2. b. Calculate and interpret the coefficient of determination.
3. c. Does the simple linear regression model appear to specify a useful relationship between these two variables? State and test the relevant hypotheses.
4. d. Predict the value of oil recovered when amount of oil added is 5.0, and do so in a way that conveys information about precision and reliability.
5. e. Without any further calculation, carry out a test of hypotheses to decide whether the value of ρ is something other than 0.