ONLY PART E) USING R SOFTWARE FOR e)

A company is said to be out of compliance if more than 8% of all invoices contain errors, and it is said to be seriously out of compliance if more than 12% of all invoices contain errors. Suppose an auditor randomly selects a sample of 800 invoices and finds that 104 contained errors.

a) Construct a 90% confidence interval for this company's error rate.

b) How should the company be rated if statements about being out of compliance or seriously out of compliance require 5% level of significance?

c) What is the probability a company would be rated as seriously out of compliance by this test if 15% of all invoices at that company contain errors?

d) What sample size should the auditor use to estimate the error rate to within 2% with 95% confidence if it is assumed that the error rate will be no more than 15%?

e) Suppose the 104 erroneous invoices can be treated as a random sample from the population of all erroneous invoices. The error amounts are contained in the file http://www.UTDallas.edu/~ammann/stat3355scripts/InvoiceErr.txt Note: since this file just contains a single set of numeric values, you can use the scan() function in R to read this data. For example,

InvErr = scan("http://www.UTDallas.edu/~ammann/stat3355scripts/InvoiceErr.txt") 

Construct a 95% confidence interval for the mean error amount. Also obtain and interpret a quantile-quantile plot of these invoice errors compared to the normal distribution.