Answer the following using R code! Answer the following using R code! The built-

Question

Answer the following using R code! Answer the following using R code!The built-in dataset rock data frame has 48 rows and 4 numeric columns of data. The data is from measurements on core samples from petroleum reservoirs. Each core sample/cross section was measured for permeability, total area of pores, total perimeter of pores, and shape. The data in the area column of rock is the data is the data we shall consider. Let the random variable X represent a random observation from rock$area. Assume the area column of rock is the outcome of a random sample of size 48 from a population with distribution X. Assume X has mean and standard deviation . Answer the following using R code:

g) Calculate the critical value to be used to produce an 97% confidence interval for using R code.

h) Find the lower boundary for a 97% confidence interval for using R code.

i) Find the upper boundary for a 97% confidence interval for using R code.

j) How long is the 97% confidence interval for using R code?

Explanation / Answer

(g)

The usual one-sample t-test in R tests the mean of a sample to a standard Normal population with unknown variance.

The critical value used to create a 97% Confidence Interval of the sample mean is: qt(.985,47)

The output is: 2.237974

(h)

So, to get a 97% confidence interval of µ we use: t.test(x,conf.level=.97)

This gives the lower boundary of the 97% confidence interval of µ will be: 6320.782

(i)

Similarly, using: t.test(x,conf.level=.97) gives the lower boundary of the 97% confidence interval of µ as: 8054.676

(j) Following the above results, to find the length of the 97% Confidence Interval we simply subtract the 97% Lower Boundary from 97% Upper Boundary; and we get 1733.894

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