Test Statistic Calculation for Investment Strategy

In a recent study, a financial analyst wants to test if a new investment strategy increases the average return of a portfolio compared to the historical average return of 8%. The analyst collects a random sample of 30 portfolios that used the new strategy and finds an average return of 9.5% with a standard deviation of 3%. Assuming the returns are normally distributed, the analyst uses a significance level of 0.05 for the hypothesis test.

To determine if the new strategy is statistically significantly different from the historical average return, the analyst will compute the test statistic, which can be found using the formula:

$$ z =\frac{ar{x} - ext{µ}}{\frac{s}{ ext{√n}}} $$

where:

• $$ ar{x} $$ is the sample mean
• $$ ext{µ} $$ is the population mean (historical average return)
• $$ s $$ is the sample standard deviation
• $$ n $$ is the sample size