do not use numpy or scippy please. Using your program from problem $1$ a$.$

homework $3$b$,$ create a Python program that assumes two different gravel manufacturers submit their

sample results to a buyer. Supplier A used the screens as described in problem$1$ whereas supplier B

used a $7/8$x$7/8$ mesh for their coarse screen and claims to have a statistically significant smaller gravel

size than supplier A$.$ You must perform a statistical $1-$sided t$-$test with an $\backslash$alpha $=0\mathrm{.}95.$ Report your findings

to the user through the command line interface

program from problem $1$

import random

import statistics

def simulate$\_$crushing$\_$operation$()$:

# Parameters

population$\_$size $=1000000$

sample$\_$size $=100$

num$\_$samples $=11$

mesh$\_$screen$1\_$size $=1$

mesh$\_$screen$2\_$size $=3/8$

# Simulate normally distributed population

population $=[$random$.$gauss$(0,1)$ for $\_$ in range$($population$\_$size$)]$

# Perform the rock crushing operation on $11$ samples

for i in range$($num$\_$samples$)$:

sample $=$ random.sample$($population$,$ sample$\_$size$)$

# Sieve the rocks based on mesh screen sizes

sieved$\_$rocks $=[$rock for rock in sample if mesh$\_$screen$2\_$size $<$ rock $<=$ mesh$\_$screen$1\_$size$]$

# Calculate sample mean and variance

sample$\_$mean $=$ statistics.mean$($sample$)$

sample$\_$variance $=$ statistics.variance$($sample$)$

# Print results

print$($f$"$Sample $\{$i $+1\}-$ Mean: $\{$sample$\_$mean$\},$ Variance: $\{$sample$\_$variance$\}")$

# Calculate the mean and variance of the sampling mean

sampling$\_$means $=[$statistics$.$mean$($random$.$sample$($population$,$ sample$\_$size$))$ for $\_$ in range$($num$\_$samples$)]$

sampling$\_$mean$\_$mean $=$ statistics.mean$($sampling$\_$means$)$

sampling$\_$mean$\_$variance $=$ statistics.variance$($sampling$\_$means$)$

# Print overall results

print$("$

Overall Results:"$)$

print$($f$"$Mean of Sampling Mean: $\{$sampling$\_$mean$\_$mean$\}")$

print$($f$"$Variance of Sampling Mean: $\{$sampling$\_$mean$\_$variance$\}")$

# Run the simulation

simulate$\_$cing$\_$operation$()$