Work in groups on these problems. You should try to answer the questions without referring to your textbook. If you get stuck, try asking another group for help.

Student Learning Outcomes

The student will calculate the 90% confidence interval for the mean cost of a home in the area in which this school is located.

The student will interpret confidence intervals.

The student will determine the effects of changing conditions on the confidence interval.

Collect the Data

Check the Real Estate section in your local newspaper. Record the sale prices for 35 randomly selected homes recently listed in the county.

NOTE

Many newspapers list them only one day per week. Also, we will assume that homes come up for sale randomly.

Complete the table:

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Describe the Data

Compute the following:

\(\bar{x}\) = _____

\(s_{x}\) = _____

\(n\) = _____

In words, define the random variable \(\bar{X}\).

State the estimated distribution to use. Use both words and symbols.

Find the Confidence Interval

Calculate the confidence interval and the error bound.

Confidence Interval: _____

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%.

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 given 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.