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\title{Stat 185 - In class problems \\
\large Wednesday, November 1}
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\begin{enumerate}
	\item In this problem, we'll play with the $t$-distribution with 12 degrees of freedom. Suppose that $X$ is a random variable with that distribution.
	\begin{enumerate}
		\item Use R to compute $P(X>1.5)$. (I guess this is called a P-value in your HW.)
		\item Use R to compute $P(|X| < 2)$.
		\item Use our $t$-distribution table to find a one-sided $t^*$ value for a 99\% level of confidence.
		\item Use R to verify your answer to the last problem.
		\item Use R to find a one-sided $t^*$ value for a 99.9\% level of confidence.
	\end{enumerate}
	
	\item Suppose we wish to estimate the average height of NC college students. We'd like a 99\% confidence interval with a margin of error half an inch.
	Pilot studies indicate that the standard deviation in  random samples is approximately 3.7 inches. How large a sample size do we need?
	
	\item McDonald's claims that a Big Mac has 560 calories. Of course, we suspect that it might be more.
	A sample of 15 Big Macs found an average of 565.88 calories with a standard deviation of 10.38.
	\begin{enumerate}
		\item Write down the hypothesis test.
		\item Compute the test statistic.
		\item Find the corresponding $p$-value.
		\item What is the conclusion of the test?
	\end{enumerate}
\end{enumerate}




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