1. Create an experiment design based on the principles discussed in tutorials to statistically show that the presence of chromium or lead in the soil reduces the rate of production of fruit in strawberry plant.
Your design should include sufficient replicates to yield a statistically significant result at 95% confidence level and 95% power.
Initial tests showed
A. a variance in the measurement of yield of 3.1 g of fruit per day.
B. presence of chromium reduced the yield of fruit of 3.0 g of fruit per day.
C. presence of lead reduced the yield of fruit of 2.4 g of fruit per day.
Your experiment design should cover what is your experimental units and observational units. You have an unlimited supply of experimental material which are the strawberry plants.
Your answer should discuss your design and how and why you made your decisions.
2. Create a sampling design to measure the fat content of muffins that are coming off a production line.
Your supervisor wants the daily average of fat content of the muffins in particular if there is any variation from day to day in the daily average during the week. Also a more detailed profile of the variation in fat content during the day (per 4 hours) is also required.
Your supervisor requires a precision of +/- 3.5 g at a confidence level of 95%. The standard deviation of a measurement is 4.1 g.
Your supervisor has allocated $150 per week with the cost of a single measurement of fat being $10.
Describe how you would take sample muffins off the production line, at what times, what days, and how many. Also discuss whether you would use only grab sampling or some composite sampling.
Your answer should discuss your decisions.
3. The local wetlands are an important fauna and flora reserve. Lately, the wetlands are being overrun by weeds and other invasive plant species. The wetlands are surrounded by a variety of land uses. An industrial estate borders the north-east corner of the wetlands through which a canal runs that empties into the wetlands. A natural park is located on the north-western corner through which a stream flows and enters the wetlands. Open field farmland, upon which animals are grazing, borders the western side of the wetlands. Finally, a housing estate is on the eastern side of the wetlands. A storm water drain empties into the wetlands from this estate. The wetlands flow further downstream from a creek locates in the south-western corner.
An environmentalist has proposed the invasion of the foreign plant species may be due to contaminants and an analyst has been employed to investigate.
A map of the wetlands and surrounds is shown below.
The analyst has to take water samples in six (6) different locations, each sample containing water and sediment, for analysis of contamination.
Copy the above map into your answer and indicate the six (6) positions you would sample, labelling them 1 - 6. For each position, explain your reasons for its position and what potential information may be obtained.