- The student will explore the properties of Confidence Intervals for Averages and gain knowledge of population standard deviation.

Summary: Note: This module is currently under revision, and its content is subject to change. This module is being prepared as part of a statistics textbook that will be available for the Fall 2008 semester.

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- The student will explore the properties of Confidence Intervals for Averages and gain knowledge of population standard deviation.

The average age for all Foothill College students for Fall 2005 was 32.7. The population standard deviation has been pretty consistent at 15. Twenty-five Winter 2006 students were randomly selected. The average age for the sample was 30.4. We are interested in the true average age for Winter 2006 Foothill College students. (http://research.fhda.edu/factbook/FHdemofs/Fact_sheet_fh_2005f.pdf)

Let

30.4

25

15=(insert symbol here)

Define the Random Variable,

the age of Winter 2006 Foothill students

What is

Is

yes

As a result of your answer to (4), state the exact distribution to use when calculating the Confidence Interval.

Normal

Construct a 95% Confidence Interval for the true average age of Winter 2006 Foothill College students.

How much area is in both tails (combined)?

0.05

How much area is in each tail?

0.025

Identify the following specifications:

**a.**lower limit =**b.**upper limit =**c.**error bound =

**a.**24.52**b.**36.28**c.**5.88

The 95% Confidence Interval is:__________________

Fill in the blanks on the graph with the areas, upper and lower limits of the Confidence Interval, and the sample mean. |
---|

In one complete sentence, explain what the interval means.

Using the same mean, standard deviation and level of confidence, suppose that

Using the same mean, standard deviation and sample size, how would the error bound change if the confidence level were reduced to 90%? Why?