If you are allowed to use a calculator it's much easier to do. I have a TI-84 plus sliver edition, for these types of problems I would go to STAT->TEST-> T-Test. Most calculators have this function. After plugging in the data I, the calculator gives you:

T-Test

mu>219

t=1.810

p=.040700

X(bar)= 232

Sx=38

n=28

The critical value is 1.81. Since the p value is less than the significance level(.1), you will Reject Ho. There is sufficient evidence to support the claim. Some teachers may want it phrased differently.

To do it by hand I would use the following equation:

t=(x(bar) - mu) *square root of n / S

Get 1.810 if plugged in data correctly.

I hope that helps.