1. ## hypothesis test help

The mean serum cholesterol level in the population of females who do not develop coronary disease is known to be 219mg. You perform an investigation as to whether the mean serum cholesterol levels in females who do develop coronary heart disease is higher than that of the disease-free population. In a sample of 28 females who have coronary disease, the sample mean serum cholest. level is xbar = 232 mg with a sample st. dev. of 38mg. At the .1 level of significance, perform the appropriate test.

Ok so the wording throws me off
are these correct?
Hnull: mu = 219
Ha: mu > 219

Also how do I go about finding the critical value, I got 1.703, but can someone tell me if that is correct or not?

Thank you!

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.