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A special diet is intended to reduce the cholesterol of patients at risk of heart disease. If the diet is effective, the target is to have the average cholesterol of this group be below 200. After six months on the diet, a simple random sample of 50 patients at risk for heart disease had an average cholesterol of 192, with standard deviation s = 21. Is this sufficient evidence that the diet is effective in meeting the target? Assume the distribution of the cholesterol for patients in this group is approximately Normal with mean μ.

The appropriate hypotheses are

An SRS of 20 recent birth records at the local hospital were selected.   In the sample, the average birth weight was 3.44 kg and the standard deviation was 0.21 kg. Assume that in the population of all babies born in this hospital, the birth weights follow a Normal distribution, with some mean μ.

We are interested in a 99% confidence interval for the population mean birth weight. The margin of error associated with the confidence interval is:

Do students tend to improve their maths SAT scores the second time they take the test? A random sample of four students who took the test twice received the following scores:

Assume that the change in maths SAT score (second score – first score) for the population of all students taking the test twice is Normally distributed, with mean μ.

The water diet requires one to drink two cups of water every half hour from when one gets up until one goes to bed, but otherwise allows one to eat whatever one likes. Four adult volunteers agree to test the diet. They are weighed prior to beginning the diet and after six weeks on the diet. The weights (in kilograms) are

For the population of all adults, assume that the weight loss after six weeks on the diet (weight before beginning the diet – weight after six weeks on the diet) is Normally distributed with mean μ.