## Related questions with answers

Although founded only in $2004$, Facebook has more than $500$ million active users, of which 50% log on to Facebook on any given day. In a recent survey by Facebook, young users (those born after 1984) were asked about their preference for delivering the news about breaking up a relationship (The Wall Street Journal, November 27-28, 2010). One of the shocking results was that only 47% of users preferred to break the news in person. A researcher decides to verify the survey results of Facebook by taking her own sample of $200$ young Facebook users. The preference percentages from Facebook and the researcher's survey are presented in the following table.

$\begin{array}{|l|c|c|} \hline \begin{array}{l} \text { Delivery } \\ \text { Method } \end{array} & \begin{array}{c} \text { Facebook } \\ \text { Results } \end{array} & \begin{array}{c} \text { Researcher's } \\ \text { Results } \end{array} \\ \hline \text { In Person } & 47 \% & 55 \% \\ \hline \text { Phone } & 30 \% & 28 \% \\ \hline \text { Email } & 4 \% & 8 \% \\ \hline \text { Facebook } & 5 \% & 3 \% \\ \hline \text { Instant Message } & 14 \% & 6 \% \\ \hline \end{array}$

At the 5% level of significance, test if the researcher's results are inconsistent with the survey results conducted by Facebook. Provide the details, using the $p$-value approach.

Solution

VerifiedFirst let us specify the two contradicting hypotheses. The null hypothesis states that

$H_0:\text{The researcher's results are consistent with the facebook results.}$

so the alternative hypothesis will be the opposite.

$H_A:\text{The researcher's results is inconsistent with the facebook results.}$

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