1- A sample of 314 patients between the ages of 38 and 82 were given a combination of the drugs ezetimibe and simvastatin. They achieved a mean reduction in total cholesterol of 0.94 millimole per liter. Assume the population standard deviation is 0.18. Construct a 90% confidence interval for the mean reduction in total cholesterol in patients who take this combination of drugs.
(2) The lifetime of a certain type of battery is known to be normally distributed with population standard deviation 20 hours. A sample of 15 batteries had a mean lifetime of 120.1 hours. Construct a 95% confidence interval for the mean lifetime for this type of battery.
3. A machine used to fill beverage cans is supposed to put exactly 12 ounces of beverage in each can, but the actual amount varies randomly from can to can. The population standard deviation is σ = 0.05 ounce. A simple random sample of filled cans will have their volumes measured, and a 99% confidence interval for the mean fill volume will be constructed. How many cans must be sampled for the margin of error to be equal to 0.01 ounce?
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