Using the regression equation $\hat{y}=5.2+2.3x$ to predict the number of visitors at a museum based on advertising dollars spent (in units of thousands), find the $90\%$ prediction interval for $x=30$ if $s_y=4.5$, $n=12$, $\bar{x}=28$, and $\sum (x_i-\bar{x}{)}^2=48$. Use the appropriate $t^{\ast }$ value for $10$ degrees of freedom.