Question

Performance of stock screeners. Recall, from Exercise 6.36 (p. 350), that stock screeners are automated tools used by investment companies to help clients select a portfolio of stocks to invest in. The data on the annualized percentage return on investment (as compared to the Standard & Poor’s 500 Index) for 13 randomly selected stock screeners provided by the American Association of Individual Investors (AAII) are repeated in the accompanying table. You want to determine whether \(\mu \) , the average annualized return for all AAII stock screeners, is positive (which implies that the stock screeners perform better, on average, than the S&P 500). An XLSTAT printout of the analysis is shown on the top of page 418.

9.0 -.1 -1.6 14.6 16.0 7.7 19.9 9.8 3.2 24.8 17.6 10.7 9.1

1. State \({H_0}\,and\,{H_a}\) for this test

Short answer

1. \(\begin{aligned}{H_0}:\mu = 0\\{H_a}:\mu > 0\end{aligned}\)

Step-by-step solution

Given Information

The sample size is 13.

\(\mu \) be the average annualized return for screeners.

Specifying the null hypothesis

The null hypothesis is given by,

\({H_0}:\mu = 0\)

Specifying the alternative hypothesis

The alternative hypothesis is given by,

\({H_a}:\mu > 0\)