**1.** Based on a random sample of 1120 adults, the mean amount of sleep per night is 7.67 hours. Assuming the population standard deviation for amount of sleep per night is 3.2 hours, construct and interpret a 90% confidence interval for the mean amount of sleep per night.

A 90% confidence interval is ( , ).

**(Round to two decimal places as needed.)
**

**2.** The random sample shown below was selected from a normal distribution.

5, 4, 7, 5, 6, 9

Complete parts a and b.

**a. **Construct a 90% confidence interval for the population mean μ.

( , ) **(round to two decimal places as needed.)**

**b.** Assume that sample mean x and sample standard deviation s remain exactly the same as those you just calculated but that are based on a sample of n=25 observations. Repeat part a. What is the effect of increasing the sample size on the width of the confidence intervals?

The confidence interval is ( , ) ** (Round to two decimal places as needed.)**

**3. **Periodically, a town water department tests the the drinking water of homeowners for contaminants such as lead. The lead levels in water specimens collected for a sample of 10 residents of the town had a mean of 2.7 mg/L and a standard deviation of 1.8 mg/L.

**a.** Construct a 90% confidence interval for the mean lead level in water specimens from the town.

( , ) **(Round to three decimal places as needed.)**