Carter’s Peanut Farm has employed you to perform a statistical analysis into the dimensional characteristics of peanuts to inform the design of a new sorting, grading and packaging plant.
You are required to undertake three studies.
Study 1:
Estimate the mean length and weight of a peanut from Carters’ latest crop. Your estimate of the mean length must be to within +/- 2 mm with an associated confidence level of 99%. You will be given real peanuts to undertake this task. You should aim to minimise the number of peanuts you measure and devise a plan to do this.
Study 2
You must use the historical data (Appendix C) and determine the variation in mean peanut length from crop to crop. You must suggesta range of peanut lengths that the new grading machine must accommodate so that over 99.5% of all peanuts can be graded.
Study 3
Use a logical argument to suggest a theoretical mathematical relationship between the length and weight of a peanut, then use the data values you obtained in the first study to ascertain the true relationship. You must then compare your results and attempt to explain any differences.
a) Write a step by step plan of how you intend to go about this task.
b) Execute your plan to obtain the results you require