From previous studies it was found that the average height of a plant is about 85 mm with a variance of 5. The area on which these studies were conducted ranged from between 300 and 500 square meters. An area of about 1 hectare was identified to study. They assumed that a population of 1200 plants exists in this 1hectare area and want to study the height of the plants in this chosen area. They also assumed that the average height in millimetre (mm) and variance of the plants are similar to that of these previous studies.  1.6.1. A sample of 100 plants was taken and

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
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From previous studies it was found that the average height of a plant is about 85 mm with a variance
of 5. The area on which these studies were conducted ranged from between 300 and 500 square
meters. An area of about 1 hectare was identified to study. They assumed that a population of 1200
plants exists in this 1hectare area and want to study the height of the plants in this chosen area.
They also assumed that the average height in millimetre (mm) and variance of the plants are similar
to that of these previous studies.


 1.6.1. A sample of 100 plants was taken and it was determined that the sample variance is 4. Find
the standard error of the sample mean but also estimate the variance of the sample mean

1.6.2. In the previous study it was found that about 40% of the plants never have flowers.
Assume the same proportion in the one-hectare population. In the sample of 100 plants the
researchers found 55 flowering plants. Find the estimated standard error of ?̂. 

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