1.The built-in R dataset \"PlantGrowth\" gives data on yields of plants, measure
ID: 3318191 • Letter: 1
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1.The built-in R dataset "PlantGrowth" gives data on yields of plants, measured by dry weight, under various treatments. We shall be interested in the weight column of the PlantGrowth dataframe. We can get the data in this column by assigning a variable to the column PlantGrowthswelght or entering the values i by 1. (You would be wise to not do the 1 by 1 entry.) Call the vector of welgh values,x. The following is a screen print of the data values: [1) 4.17 5.58 5.18 6.11 4.50 4.61 5.17 4.53 5.33 5.14 4.81 4.17 4.41 3.59 5.87 [16) 3.83 6.03 4.89 4.32 4.69 6.31 5.12 5.54 5.50 5.37 5.29 4.92 6.15 5.80 5.26 de for assigning the e t elumn to vector x Assume these values are a random sample from a normal population with distribution x. Assume x has mean and standard deviation o The is xe-PlantGrowthsweight. Answer the following using R code:Explanation / Answer
e) mean of (3/2) x = 3/2 * mean(x) = 3/2 * 5.073 = 7.6095
f) x<-PlantGrowth$weight
mu=mean(x)
sd=sd(x)
z<-qnorm(0.5+0.98/2)
n=length(x)
Lower limit = mu-sd*z/sqrt(n) = 4.775182
Upper Limit= mu+sd*z/sqrt(n) = 5.370818
g) z = (mu-5)*sqrt(30)/sd
We get z= 0.5702255. At 2% significance, z* = 2.053749. Since z<z*, we fail to reject H0. ie, mu=5
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