91影视

Referring to exercise 2.44, the stock screeners are automated tools used by learned that stock screeners are automated tools used by investment companies to help clients select a portfolio of stocks to invest in.

a.

The sample mean is,

\(\begin{aligned}\bar x &= \frac{{\sum\limits_{i = 1}^n {{x_i}} }}{n}\\ &= \frac{1}{{13}}\left( {9 + \left( { - 0.1} \right) + \left( { - 1.6} \right) + ... + 9.1} \right)\\ &= \frac{{140.7}}{{13}}\\ &= 10.823076\\ \approx 10.82\end{aligned}\)

The sample standard deviation is,

\(\begin{aligned}s &= \frac{1}{{n - 1}}\left( {{{\sum\limits_{i = 1}^n {\left( {{x_i} - \bar x} \right)} }^2}} \right)\\ &= 7.7115\\ \approx 7.71\end{aligned}\)

The 90% confidence interval is,

\(\begin{aligned}100\left( {1 - \alpha } \right)\% &= 90\% \\\left( {1 - \alpha } \right) &= 0.90\end{aligned}\)

So,

\(\begin{aligned}\alpha &= 0.1\\\frac{\alpha }{2& = 0.05\end{aligned}\)

Therefore, the 90% confidence interval is,

\(\begin{aligned}C.I &= \bar x \pm {t_{n - 1,\frac{\alpha }{2}}}\frac{s}{{\sqrt n }}\\ &= 10.82 \pm {t_{12,0.05}}\frac{{7.71}}{{\sqrt {13} }}\\ &= 10.82 \pm \left( {1.782 \times 2.138} \right)\\ &= 10.82 \pm 3.810\\ &= \left( {7.01,14.63} \right)\end{aligned}\)

Hence, a 90% confidence interval for the average annualized percentage return on investment of all stock screens provided by AAII is\(\left( {7.01,14.63} \right)\).

90% confidence that the average annualized percentage return on investment of all stock screeners provided by AAII will lie either in the interval \(\left( {7.01,14.63} \right)\) or it is not.

b.

For the confidence interval \(\left( {7.01,14.63} \right)\), there is a 90% chance to AAII stock screeners perform better than the S&P 500.

c.

It can be concluded that the assumption about the distribution of annualized percentage returns from investment is required for inference part b to be valid is that the distribution is normal.

From the above graph, it can be concluded that the assumption is reasonably satisfied.