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U. P. Enpayne is a urologist specializing in kidney stones. U. P. has a theory that the incidence of kidney stones is affected by the amount of calcium in the local drinking water. U. P. conducted two studies in different areas with low and high calcium and obtained the following results:

**Low Calcium Area**

A sample of 400 people in this area showed that 20 had suffered from kidney stones.

Construct a 50% confidence interval on the proportion of people in this area who suffer from kidney stones.

**High Calcium Area**

A sample of 400 people from this area showed that 40 had suffered from kidney stones.

Can U. P. prove that the low calcium area has a lower incidence of kidney stones than the high calcium area at the .01 level of significance? ? What are the null and alternative hypotheses. **Plug the values into the Z _{TEST }formula**. Use Z

Find the p-value from part b.

Solution:

a) Solution:

To construct a 50% confidence interval on the proportion of people in the low calcium area who suffer from kidney stones, we can use the following formula:

Confidence interval = sample proportion ± (z-value)*(standard error)

where z-value corresponds to the level of confidence and standard error is given by: