Aphid infestation of fruit trees is usually controlled either via pesticides or via ladybug innundation. In a particular area, 2 different (and well isolated) groves, with 15 fruit trees each, are selected for an experiment. The trees in both groves are of the same age, roughly the same size, and can be assumed to be independent. One grove is sprayed with pesticides, and one is flooded with ladybugs. The fruit yield (in pounds) for each tree is given below:
Pesticide trees:
55.57109 36.50319 47.80090 33.34822 36.16251
35.28337 41.50154 44.18931 40.81439 33.88648
44.90427 49.97089 22.85414 27.84301 38.49843
Ladybug trees:
45.44505 35.52320 46.97865 45.76921 41.66216
54.69599 58.77678 49.08538 48.53812 70.17137
51.86253 39.59365 42.10194 47.39945 39.04648
a) Plot the histograms of the yields in the two groves
b) Comment on the histogram shapes. Which densities do they resemble? In particular, do they appear normal?
c) Find the sample means of yields for the two groves
d) Using your conclusion in (b) and answer in (c), provide the two 95% confidence intervals for the true mean yields for trees under the two treatments.
e) Interpret one of the confidence intervals you constructed.
f) Find the sample variances for the yields in the two groves
g) We have learned how to construct confidence intervals for the variance of a normal distribution -- we do that using a chi-square distribution. For the grove(s) with approximately normal yield, construct the 95% confidence interval for the true variance of yield.