The student will calculate the 90% confidence interval for the average cost of a home in the area in which this school is located.
The student will interpret confidence intervals.
The student will examine the effects that changing conditions has on the confidence interval.
Collect the data
Check the Real Estate section in your local newspaper or website. (Note: many papers only list them
one day per week. Also, we will assume that homes come up for sale randomly.) Record thesales prices for 35 randomly selected homes recently listed in the county.
Complete the table:
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Describe the data
Compute the following:
A
$\overline{x}$ =
B
${s}_{x}$ =
C
$n$ =
Define the Random Variable
$\overline{X}$ ,
in words.
$\overline{X}$ =
State the estimated distribution to use. Use both words and symbols.
Find the confidence interval
Calculate the confidence interval and the error bound.
A
Confidence Interval:
B
Error Bound:
How much area is in both tails (combined)?
$\alpha $ =
How much area is in each tail?
$\frac{\alpha}{2}$ =
Fill in the blanks on the graph with the area in each section. Then, fill in the number
line with the upper and lower limits of the confidence interval and the sample mean.
Some students think that a 90% confidence interval contains 90% of the data. Use the list of data on the
first page and count how many of the data values lie within the confidence interval. What percent is this?Is this percent close to 90%? Explain why this percent should or should not be close to 90%.
How many house prices would be needed in the sample to ensure that the error was no more than $2000 for the 90% confidence interval?
Describe the confidence interval
In two to three complete sentences, explain what a Confidence Interval means (in general),
as if you were talking to someone who has not taken statistics.
In one to two complete sentences, explain what this Confidence Interval means for this
particular study.
Use the data to construct confidence intervals
Using the above information, construct a confidence interval for each confidence level given.
Confidence level
EBM / Error Bound
Confidence Interval
50%
80%
95%
99%
What happens to the EBM as the confidence level increases? Does the width of the confidence interval increase or decrease? Explain why this happens.
Effect of an outlier
Suppose one of the values input incorrectly. Choose one data value and increase the amount by adding two extra zeroes.
Calculate the 90% confidence interval: _____________
Calculate the Error Bound: ____________
How does the outlier effect the width of the confidence interval?
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