The average life expectancy for Bostonians is 73 years. Assume that this average

Question

The average life expectancy for Bostonians is 73 years. Assume that this average was based on a sample of 150 Bostonians and that the population standard deviation is 3.7 years. Construct a 98% confidence interval for the population average life expectancy of Bostonians. According to a recent survey, high school girls average 100 text messages daily. Assume that the survey was based on a random sample of 30 high school girls. The sample standard deviation is computed as 20 text messages daily. What is the 95% confidence interval of the population mean texts that all high school girls send daily? Now calculate- the same confidence interval as (b), but with a sample size of 501. What did increasing the sample size do to our margin of error? What effect did it have on the preciseness of our interval estimate?

Explanation / Answer

b.The standard error of mean is:

Root over s^2/n

=root over 20^2/30=3.65

The 95% confidence interval is:

X bar+/-t(0.95,29)*Sm/root over n

=100+/-2.0452*3.65/root over 30

=100+/-1.36

=(98.64,101.36)

a.The 98% confidence interval is:

x bar+/-z(0.98)*sigma/root over n

=73+/-2.33*3.7/root over 150

=73+/-1.22

=(71.78,74.22)

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