Test Statistic Calculation for Hypothesis Testing

In a recent study, a financial analyst sought to identify whether the average return on a particular stock is greater than the average return of the market. A sample of 50 returns from the stock showed a sample mean ($ar{x}$) of 12% with a sample standard deviation ($s$) of 8%. The average market return is known to be 9%.

To test the hypothesis, the analyst sets up the following null and alternative hypotheses:

Null Hypothesis ($H_0$): $ar{x} ext{ } ext{is less than or equal to } 9 ext%$

Alternative Hypothesis ($H_1$): $ar{x} ext{ } ext{is greater than } 9 ext%$

Using a significance level of $eta = 0.05$, calculate the test statistic to determine whether the evidence supports rejecting the null hypothesis.