## Related questions with answers

A mutual fund is a professionally managed investment that can be sold to the general public. The following table lists the 3-month rates of return, in percent, for samples of healthcare-related and technology-related mutual funds, as reported by Morningstar, an independent investment research company.\

$\begin{array}{lcccr|ccccc} \hline {\text { Healthcare}} & {\text { }} &{\text { }} &{\text { }} &{\text { }} &{\text { Technology }} \\ \hline 9.7 & 9.5 & 7.6 & 6.8 & 6.7 & 6.5 & 6.4 & 6.4 & 6.2 & 4.9 \\ 6.7 & 6.6 & 4.6 & 3.9 & 3.9 & 4.6 & 4.6 & 4.2 & 3.6 & 3.2 \\ 3.7 & 3.3 & 3.0 & 0.8 & -9.9 & 2.9 & 2.8 & 2.7 & 2.5 & \\ \hline \end{array}$

a) Use the technology of your choice to obtain normal probability plots and boxplots for the two samples.

b) Is it reasonable to use the pooled t~test to perform a hypothesis test here? Explain your answer.

c) Is it reasonable to use the Mann-Whitney test to perform a hypothesis test here? Explain your answer.

Solution

Verified(a) $\textbf{Normal probability plot}$

The data values are on the horizontal axis and the standardized normal scores are on the vertical axis.

If the data contains $n$ data values, then the standardized normal scores are the z-scores in the normal probability table of the appendix corresponding to an area of $\dfrac{j-0.5}{n}$ (or the closest area) with $j\in \{1,2,3,....,n\}$.

The smallest standardized score corresponds with the smallest data value, the second smallest standardized score corresponds with the second smallest data value, and so on.

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