```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = FALSE)
```

For the problems in which calculations are needed, please include your \texttt{R} code with your answers, otherwise you will not be given full credit.  Please upload your assignment by Friday, January 27, 11:59 pm in either a HTML, pdf, or Word document to Sakai.

- 1.
Assume that $Z$ is a random variable from the standard normal (i.e. $\mu = 0$, $\sigma = 1$).

-- a.
Calculate $P(Z \geq -1)$.
```{r}
# Write your R code to answer the question here.
```
-- b.
Determine the $0.2-$quantile of $Z$.
```{r}
# Write your R code to answer the question here.
```

- 2.
$F_{a,b}$ is a random variable from the $F$-distribution with $df1 = a$ and $df2 = b$.

-- a.
Calculate $P(F_{5,40} \leq 2.9)$
```{r}
# Write your R code to answer the question here.
```
-- b.
Find $x$ such that $P(F_{6,24} \geq x) = 0.05$
```{r}
# Write your R code to answer the question here.
```

- 3.
Given a dataset of scores $\{0,2,5,6,3,3,3,1,4,3\}$, calculate the

-- a.
mean,
```{r}
# Write your R code to answer the question here.
```
-- b.
median,
```{r}
# Write your R code to answer the question here.
```
-- c.
variance.
```{r}
# Write your R code to answer the question here.
```

- 4.
A random sample of 32 persons attending a certain diet clinic was found to have lost an average of 30 pounds over a three week period, with a sample standard deviation of 11 pounds. For these data

-- a.
Calculate a 99% confidence interval for the given data.
```{r}
# Write your R code to answer the question here.
```
-- b.
Interpret the confidence interval in the context of the given problem.

-- c.
Suppose I wished to test my current belief that the average weight loss of the population is equal to 28 pounds.  I come to the conclusion to reject $H_0: \mu = 28$.  Based on your answer to (b), does this make sense?  Why or why not?

- 5.
An outbreak of Salmonella-related illness was thought to be caused by pre-cut melons from a specific factory.  Several samples were collected and can be found in the file \texttt{salmonella.csv} on the course webpage.  A Salmonella level (in MPN/g) greater than 0.3 MPN/g is considered dangerous. To demonstrate that the levels are safe we want to show the mean level is less than 0.3 MPN/g.

-- a.
State the null and directional alternative hypothesis in symbols.  Explicitly define $\mu$.

-- b.
Find the test statistic and p-value for the data below.  Be sure to clearly identify them from your output.  Note you are performing a one-sided test.
```{r}
# Write your R code to answer the question here.
```

-- c.
State your decision and conclusion for the given problem.

