Based on a random sample of 1120 ​adults, the mean amount of sleep

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.)

Here’s the SOLUTION

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