Name: __Sarah Gallimore_____ Module 8 – Stratified and Double Sampling Assignment 1. What are the three approaches for recombining data in double sampling? What assumptions must be met in order to...

Questions 4-9


Name: __Sarah Gallimore_____ Module 8 – Stratified and Double Sampling Assignment 1. What are the three approaches for recombining data in double sampling? What assumptions must be met in order to utilize each of them? (6 pts) · Ratio Estimation – The ratio of means and mean of ratios requires that the intercept of a regression through the x and y passes very close to the origin. · Regression Estimation – Need a precise estimate of population mean, mostly liner relationships between x and y, and the variance of y about the regression line should be about the same as the values of x. 2. If we are working with a dataset and each of the double sampling recombination techniques will produce an unbiased estimate, how do we determine which technique to use? (6 pts) If all of the recombination techniques will produce an unbiased estimate, then you should use the technique with the smaller variance. 3. Explain the purpose of stratification, and provide three reasons we may want to use it. (5 pts) The purpose of stratification is to take advantage of prior knowledge when designing a study. · Ensuring the sample is representative across the frame. · Controlling the variation. · Allowing different designs within sub populations. Strata Strata Area (acres) Std. dev. 1 22 20 2 48 65 3 95 45 4 55 35 4. For the provided data in Excel, determine how many of our possible 120 – 1/10th acre plots should be allocated using optimal allocation for each strata. (4 pts) 5. Based on the data provided in Excel of 1 m2 quadrat samples of biomass (kg/m2) from three strata, determine the combined mean biomass per hectare (Mg/hectare) and its associated variance. Assume that stratums one, two, and three are 35, 42, and 60 hectares, respectively. Determine if you need to account for the finite population correction factor. Does this seem to be a good stratification? Support your answer based on your calculations. (12 pts) 6. You have been assigned to design a systematic monitoring program for the assessment of range forage biomass and present it to your boss. The only guidance he provided you is that there are 46,000 acres to inventory, you need a sampling intensity that would equal measuring 0.005%. You decide to give options of different size fixed area plots, complete the table below in chains. (5 pts) Square Spacing Rectangular Spacing Plot Size ft2 n L B L B 20 40 7. For the given dataset of 1 m2 forage estimates (kg/m2), calculate the regression gradient (b) between the 2014 and 2016 estimates and determine if regression estimation is appropriate for estimating the 2016 (y value) population average (Mg/hectare). The data is available in the accompanying Excel file. (10 pts) 8. From question #7, calculate the 2016 population average and variance of forage (Mg/hectare), assuming the population is 32 hectares. Then construct a 90% confidence interval for the population mean and write a statement about your confidence in the estimate. (12 pts) 9. By looking at the given x, y data pairs, determine if either ratio estimation, regression estimation, difference estimation, or all of them can be used in estimating the y variable population total. Remember to look at the requirements for using each of these techniques and justify your answers based on these requirements. The data is available in the accompanying Excel file. (5 extra credit points)