In a test to compare the effectiveness of two drugs designed to lower cholesterol levels, 75 randomly selected patients were given drug A and 100 randomly selected patients were given drug B. Those given drug A reduced their cholesterol by an average of 40 with a standard deviation of 12, and those given drug B reduced their levels by an average of 42 with a standard deviation of 15. The units are milligrams of cholesterol per deciliter of blood serum.Can you conclude (as the manufacturer claims) that the mean reduction using drug B is greater than drug A. Conduct an appropriate hypothesis test at a=0.05.

The compressive strength in kilopascals, was measured for concrete blocks from five different batches of concrete, both three days and six days after pouring. The data is presented in the following table. Can you conclude (at a=0.05) that the mean strength after 6 days is greater than the mean strength after 3 days. Assume an approximately normal distribution.

Batch 1 2 3 4 5

After 3 days 1341 1316 1352 1355 1327

After 6 days 1376 1373 1366 1384 1358