An article in Technometrics $(1999,$ Vol. $41,$ pp$.202211)$ studied the capability of a gauge by measuring the weight of paper. The data for repeated measurements of one sheet of paper are as follows:

$3\mathrm{.}4813\mathrm{.}4483\mathrm{.}4853\mathrm{.}4753\mathrm{.}4723\mathrm{.}4773\mathrm{.}4723\mathrm{.}4643\mathrm{.}4723\mathrm{.}4703\mathrm{.}4703\mathrm{.}4703\mathrm{.}4773\mathrm{.}4733\mathrm{.}474$

Assume that the data is normally distributed.

$```\{$r$\}$

#a$)$ Is there sufficient evidence to claim that the the measurement standard deviation is less than $0\mathrm{.}01$ grams at $=0\mathrm{.}05?$ Use a proper hypothesis test R function.

#HINT: you need to load package "EnvStats" first by run this code: library$($EnvStats$)$

#Your code starts here

# Step $0$: load package $$EnvStats$$

library$($EnvStats$)$

# Step $1$: create a vector x to store all provided measurements

# Step $2$: perform the hypothesis test using a proper R function

$```$

$**$Analysis$**$:

#Based on the Step $2$ R function output,draw conclusion and make interpretation

$```\{$r$\}$

#b$)$ Verify and PRINT the P$-$value in the R function output of part $($a$).$

#Your code here