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 Î¼ and standard deviation
Ïƒ. Answer the following using R code:
g) Calculate the critical value to be used to produce an 97%
confidence interval for Î¼.
h) Find the lower boundary for a 97% confidence interval for
i) Find the upper boundary for a 97% confidence interval for
j) How long is the 97% confidence interval for Î¼?