In her exploration of grass flavors, Leticia sets up the following study. She pl
ID: 3260804 • Letter: I
Question
In her exploration of grass flavors, Leticia sets up the following study. She plants two acres with grass, one using the old grass her goats have always eaten and the other using a new variety. Tastyweed^TM. Each acre is then mowed to the Same height and divided into fifty equal pens. Lastly, a randomly Selected goat is allowed to graze in each pen (that's a different goat in each pen) for three hours and the height of the grass is again measured. The heights of the old grass are averaged, as well as the heights of the Tastyweed^TM. a. What kind of design is employed here? Be as detailed as possible. b. What is(are) the populations) of interest? c. What is(are) the variable(s)? State type and level of measurement as well. d. The mean height of the Tastyweed^TM was much lower after the goats had eaten their fill than the old grass. Is it safe to assume that Leticia's goats prefer Tastyweed^TM? Why or why not?Explanation / Answer
Solution
Part (a)
The design is Completely Randomised Design (CRD). Two treatments, namely ‘old grass’ and ‘Tastyweed’ are being compared with 50 observations per treatment.
Part (b)
The populations are:
1. Quantity of grass eaten by the goat under ‘old grass’ treatment
2. Quantity of grass eaten by the goat under ‘Tastyweed’ treatment
In both populations, the quantity is measured by the difference in the height of grass before and after the grazing by the goat.
Taking the difference in the height of grass before and after the grazing by the goat as a measure of quantity of grass eaten by the goat is fully justified since
Part (c)
The variables are:
X, represented by xi = difference in the height of grass before and after the grazing by the ith goat (which is also the same as the ith pen) under ‘old grass’ treatment.
Y, represented by yi = difference in the height of grass before and after the grazing by the ith goat (which is also the same as the ith pen) under ‘tastyweed’ treatment.
Both variables are continuous and can also be assumed to follow Normal Distribution.
The statistic for comparison would be the means of X and Y.
Part (d)
A statistically significant difference between the means of X and Y, as defined under Part (c) would definitely mean that the ‘Tastyweed’ is preferred by the goats since as justified under Part (b), significant difference between the means of X and Y implies significant difference between the means of quantity of grass eaten by the goats and quantity of grass eaten by the goats is naturally an indicator of taste of the grass DONE