---
title: "Homework assignment #12"
author: "Milica Cudina"
date: "`r Sys.Date()`"
output: pdf_document
---
<!-- The author of this template is Dr. Gordan Zitkovic.-->
<!-- The code chunk below contains some settings that will  -->
<!-- make your R code look better in the output pdf file.  -->
<!-- If you are curious about what each option below does, -->
<!-- go to https://yihui.org/knitr/options/ -->
<!-- If not, feel free to disregard everything ...  -->
```{r echo=FALSE, warning=FALSE, include=FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  fig.align="center",
  fig.pos="t",
  strip.white = TRUE,
  tidy = TRUE
)
```
<!-- ... down to here. -->

---

## Problem #1 ($2$ points)
Solve **Exercise 7.2** from the textbook.


## Problem #2 ($2+2=4$ points)
Solve **Exercise 7.4** from the textbook **assuming a two-sided alternative**.


## Problem #3 ($1+1+2=4$ points)
Solve **Exercise 7.6** from the textbook. 


## Problem #4 ($2$ points)
Solve **Exercise 7.10** from the textbook.


## Problem #5  ($2+4+4=10$ points)
Solve **Exercise 7.12** from the textbook. 


## Problem #6 ($4$ points)
Solve **Exercise 7.16** from the textbook. 


## Problem #7 ($3$ points)
Solve **Exercise 7.18** from the textbook. 


## Problem #8 ($4+2+1=7$ points)
Solve **Exercise 7.22** from the textbook. 


## Problem #9 ($7$ points)
*Source: ``Probability and Statistics for Engineers and Scientists'' by Walpole, Myers, Myers, and Ye.* 
  The contents of seven similar containers of sulfuric acid are
\begin{equation}%\label{}
    \nonumber 
    \begin{split}
      9.8, \quad 10.2, \quad 10.4, \quad 9.8, \quad 10.0, \quad 10.2,
      \quad 9.6
    \end{split}
\end{equation}
liters. Find a 95\%-confidence interval for the mean contents of all
such containers, assuming a normal distribution of the contents of all
such containers.  


## Problem #10 ($7$ points)
*Source: ``Probability and Statistics for Engineers and Scientists'' by Walpole, Myers, Myers, and Ye.* 
  The Edison Electric Institute has published figures on the number of
  kilowatt hours used annually by various home appliances. It is
  claimed that a vacuum cleaner uses an average of $46$ kilowatt hours
  per year. If a random sample of $12$ homes included in a planned
  study indicates that vacuum cleaners use an average of $42$ kilowatt
  hours per year with a standard deviation of $11.9$ kilowatt hours,
  do these data suggest that at the $0.05$ significance level the mean
  annual usage of vacuum cleaners is less than $46$ kilowatt hours?
  Assume the population distribution of usage in kilowatt hours to be
  normal.