## Related questions with answers

In a study to determine whether counseling could help people lose weight, a sample of people experienced a group-based behavioral intervention, which involved weekly meetings with a trained interventionist for a period of six months. The following data are the numbers of pounds lost for $14$ people, based on means and standard deviations given in the article.

$\begin{array}{rrrrrrr} \hline 18.2 & 24.8 & 3.9 & 20.0 & 17.1 & 8.8 & 13.4\\ 17.3 & 33.8 & 29.7 & 8.5 & 31.2 & 19.3 & 15.1\\ \hline \end{array}$

$\textbf{a.}\hspace{10pt}$ A boxplot shows these data. Is it reasonable to assume that the conditions for performing a hypothesis test are satisfied? Explain.

$\textbf{b.}\hspace{10pt}$ If appropriate, perform a hypothesis test to determine whether the mean weight loss is greater than $10$ pounds. Use the $\alpha = 0.05$ level of significance. What do you conclude?

Solution

VerifiedFrom the given, we have

$\begin{aligned} 18.2\quad 24.8\quad 3.9\quad 20.0\quad 17.1\quad 8.8\quad 13.4\\ 17.3\quad 33.8\quad 29.7\quad 8.5\quad 31.2\quad 19.3\quad 15.1 \end{aligned}$

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