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\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.  \item This doesn't prove the hypothesis but we can say that the data support it.  \end{itemize}  If our null hypothesis was different than p=0.35, lets say p=30 and our sample yields $\hat{p}$, then the data are not consistent with the hypothesis and we need to mke choices as to whethere this inconsistency is large enough to not believe the hypothesis.  \begin{itemize}  \item If the inconsistency is significant, we reject the null hypothesis  \end{itemize}  \subsection{Example for hypothesis testing for one proportion}  Research conducted a few years ago showed that 35$\%$ of UCLA students had travelled outside the US. UCLA has recently implemented a new study abroad program and results of a new survey show that out of the 100 randomly sampled students 42 have travelled abroad. Is there significant evidence to suggest that the proportion of students at UCLA who have travelled abroad has increased after the implementation of the study abroad program?  \begin{itemize{  \item population proportion used to 0.35  \item new sample proportion is 0.42  \item Testing the claim that the population proportion is now greater than 0.35 .  \item But is this difference statistically significant, i.e. are the data inconsistent enough?  \item We do a formal hypothesis test to answer this question.  \end{itemize}  \section{Setting up Hypotheses}  \begin{itemize}  \item Null hypothesis, denoted by Ho, specifies a population model parameter of interest and proposes a value for that parameter (p). \[H_0: p=0.35\]  \item Alternative hypothesis, denoted by HA, is the claim we are testing for.\[H_A :p > 0.35\]  \item Even though we are testing for the alternative hypothesis, we check to see whether or not the null hypothesis is plausible.  \item If the null hypothesis is not plausible, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative. If the null hypothesis is plausible, we fail to reject the null hypothesis and conclude that there isn't sufficient evidence to support the alternative.  \end{itemize}