I have a question for an exam:
You read a journal article on TOTAL-cholesterol, HDL-cholesterol and LDL-cholesterol from a study of n=100 patients where TOTAL-cholesterol = HDL + LDL cholesterol. Assume that for HDL, LDL and TOTAL cholesterol, the distributions are iid multivariate normal.
The article reports for:
HDL: sample-mean = 145 and p-value for the population mean to be 150 is 0.10
LDL: sample-mean = 48 and p-value for the population mean to be 50 is 0.05
TOTAL: sample-mean = 193 and p-value for the population mean to be 200 is 0.05 All P-values are Two-Sided
You must derive the standard deviations and covariances for HDL-cholesterol and LDL-cholesterol in a single observation from this information
A. Work backwards from the p-values for the population means be equal to the specified values based on the observed sample means to obtain the standard deviations for both HDL-cholesterol and LDL-cholesterol in a single observation?
B. What is the covariance of HDL and LDL cholesterol in a single observation?
How does one figure out the standard deviation with only the information given is the mean and p-value?