1.6. From previous studies it was found that the average height of a plant is about 85 mm with a varianceof 5. The area on which these studies were conducted ranged from between 300 and 500 squaremeters. An area of about 1 hectare was identified to study. They assumed that a population of 1200plants exists in this lhectare 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 similarto 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. Findthe standard error of the sample mean but also estimate the variance of the sample mean1.6.2. 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 theresearchers found 55 flowering plants. Find the estimated standard error of p.1.7. Refer to information in 1.6 The one-hectare plot has different types of vegetation - shady areas,sunny areas. The researchers want to establish whether the type of vegetation has an influence onthe mean height of the flower. They noticed that the two areas are more or less the same size andthe plants were spread evenly over the two areas. Recall the assumption of 1200 plants on this1hectare plot. The researchers decide to investigate the shady and the sunny areas in order toevaluate the mean heights as well record the number of flowering and non-flowering plants. Asample of 20 plants was taken from the sunny area and a sample of 25 from the shady area. Themean heights were 85 mm and 75 mm respectively and variances, 4 and 6 respectively. The3following steps were undertaken. Show how it applies to this case.•Establish that the plot needs to be divided according to vegetation -strata•Identify the different strata i = 1,2,...,!N₁Find the weight of each stratum W₂ =N•Take a sample from each stratum 7₁, n2,..., nFind the sample mean of each stratum X₁ni2i=1 Xll.Find the variance of each stratums} = 12"t(X - Xy)2n-1Estimate the stratified mean Xs = 1 W₁ X₁ as estimation of the population mean μ.Estimate the standard error of the stratified mean.●•

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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