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# Stripes on Leaves

GMAT-EFUKYE

A certain species of tree has striped leaves. The number of stripes per leaf varies, but 100 leaves sampled from one particular cluster of trees yielded an average number of stripes per leaf of 10.2, with a margin of error of 4.1 stripes. The graph below shows that each of the 100 leaves had between 7 and 14 stripes (at $t = 0$).

Seeds of this species of tree were planted in two different environments. The first environment had sparse vegetation and low annual rainfalls. The second environment had more ground-level vegetation and higher annual rainfalls.

After 4 years, 50 leaves from the trees grown in each environment were selected. The number of stripes on each leaf was recorded.

After 8 years, 50 more leaves were selected from trees in each environment. By this time, the number of stripes tended to cluster into two distinct groups. This pattern continued through a time measurement 12 years after the initial seeding. In both the 8 year and 12 year measurements, the cluster of lower stripe counts was observed from the environment with low rainfall.

The graph of the number of stripes recorded is given below:

The average number of stripes recorded during years 4, 8 and 12 are as follows:

Year 4 8 12
Low Rainfall Environment 13.6 11.2 7.5
High Rainfall Environment 14.1 19.3 23.6

Part 1:
For trees grown in the environment with higher rainfall, is the margin of error of the number of stripes expected to increase, decrease, or remain roughly the same?

Part 2:
What is the percentage decrease in the mean number of stripes over the time period from 4 years to 12 years for leaves of trees in low rainfall?

Part 3:
What is the average rate of increase (as measured in stripes per year) in the mean number of stripes for leaves of trees in the high rainfall environment from 4 years to 12 years?