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\item We are 95$\%$ confident that the true population proportion of UCLA students who travelled outside the US is between 26$\%$ and 44$\%$.  \item 95$\%$ of random samples of size n = 100 will produce confidence intervals that contain the true population proportion.  \end{itemize}  \begin{itemize}  \item The true population proportion,p, may be outside the interval,but we would expect it to be somehwat close to $\hat{p}$  \item In our random sample of 100 students we had found that 35 of them have at some point in their lives travelled outside the US,$\hat{p}$= 0.35.  \item It is difficult to decide how close is close enough, or how far is too far, and this decision should not be made subjectively.  \end{itemize}  \section{Hypothesis Testing}  \begin{itemize}  \item In Statistics when testing claims we use an objective method called hypothesis testing  \item Given a sample proportion,  , and sample size, n, we can test claims about the population proportion, p.  \item We call these claims hypotheses  \item Our starting point, the status quo, is called the null hypothesis and the alternative claim is called the alternative hypothesis.  \item If our null hypothesis was that p = 0.35 and our sample yields  = 0.35, then the data are consistent with the null hypothesis, and we have no reason to not believe this hypothesis.  \end{itemize}