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Confidence Intervals: Confidence Interval Lab I (edited: Teegarden)

Module by: Mary Teegarden Based on: Confidence Intervals: Confidence Interval Lab I by Dr. Barbara Illowsky, Susan Dean

Summary: Labs changed to incorporate mini-tabs.

Class Time:

Name:

Student Learning Outcomes:

  • 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 the sales prices for 35 randomly selected homes recently listed in the county.

  1. Complete the table:
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________

Describe the Data

  1. Compute the following:
    • a. x¯ x =
    • b. s x s x =
    • c. n n =
  2. Define the Random Variable X¯ X , in words. X¯ X =
  3. State the estimated distribution to use. Use both words and symbols.

Find the Confidence Interval

  1. Calculate the confidence interval and the error bound.
    • a. Confidence Interval:
    • b. Error Bound:
  2. How much area is in both tails (combined)? αα =
  3. How much area is in each tail? α 2 α 2 =
  4. 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.
    Figure 1
    Normal distribution curve with two vertical upward lines from the x-axis to the curve. The confidence interval is between these two lines. The residual areas are on either side.
  5. 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%.
  6. 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

  1. 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.
  2. In one to two complete sentences, explain what this Confidence Interval means for this particular study.

Use the Data to Construct Confidence Intervals

  1. Using the above information, construct a confidence interval for each confidence level given.
    Confidence level EBM / Error Bound Confidence Interval
    50%    
    80%    
    95%    
    99%    
  2. 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.

  1. Calculate the 90% confidence interval: _____________
  2. Calculate the Error Bound: ____________
  3. How does the outlier effect the width of the confidence interval?

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