# 8.11 Confidence interval lab 4

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This lab incorporate both lab 1 and lab 2 with minitab.

Confidence Interval Lab

Name:

## Student learning outcomes:

• The student will calculate the 90% confidence intervals.
• The student will interpret confidence intervals.
• The student will examine the effects that changing conditions has on the confidence interval.
• The student will examine the relationship between the confidence level and the percent of constructed intervals that contain the population average.

## 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 36 randomly selected homes recently listed in the county and indicate whether you found them in the paper or on the website. Include the reference.

Complete the table:

## Describe the data

1. Compute the following: (include the session window)

$\overline{x}$ = s = n =

2. Define the Random Variable $\overline{X}$ in words:

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

## Find the confidence interval

1. Using Minitab, calculate the 90% confidence interval and determine the error bound. (include in the session window)

a. Confidence Interval:

b. Error Bound:

2. How much area is in both tails (combined)? α =

3. How much area is in each tail? $\frac{\alpha }{2}$ =

4. Using Minitab, create the graph for the 90% confidence interval created above. (Graph → Prbability Distribution Plot→View Probability) Include the graph with this lab.

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. (include the session window information)

 Confidence Level Error Bound Confidence Interval 85% 95% 98% 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. (include in the session window)

1. Calculate the 90% confidence interval: _____________

2. Calculate the Error Bound: ____________

3. How does the outlier affect the width of the confidence interval? Use complete sentences.

## Part ii

Heights of 100 Women (in Inches)

 59.4 63.8 61.8 61.3 61.5 62.9 64.3 60.8 57.9 64 71.6 62.9 60.6 59.2 64.3 63.1 65 65.5 58.5 66.4 69.3 63 69.8 64.1 62.9 62.2 64.1 62.3 63.4 61.2 65 63.9 60 59.3 60.6 58.7 61.1 65.5 69.2 60.4 62.9 68.7 64.9 64.9 63.8 64.7 65.3 64.7 65.9 58.7 66.5 65.5 66.1 62.4 58.8 66 64.6 58.8 62.2 66.7 61.7 61.9 66.8 63.5 64.9 60.5 59.2 66.1 60 67.5 55.2 69.6 60.6 60.9 65.7 64.7 61.4 64.9 58.1 63.2 67.2 58.7 65.6 63.3 62.5 65.4 62 66.9 62.5 56.6 66.5 63.4 63.8 66.3 70.9 60.2 63.5 57.9 62.4 67.7

1. Listed above are the heights of 100 women. These are in the student data file in the lab. Use MiniTab to randomly select 10 data values. (Calc → Random data → data from a column)

2. Calculate the sample mean and sample standard deviation and record our answer below. Assuming that the population standard deviation is known to be 3.3. Construct a 90% confidence interval for your sample of 10 values. Write the confidence interval you obtained below.

3. Repeat #1 and #2 nine more times, and record the 90% confidence interval for each of your samples. (Note: since you are randomly selecting the 10 data values you may use the same one in more than one sample. Include this portion of your session window)

• $\overline{x}$ = s = CI =
• $\overline{x}$ = s = CI =
• $\overline{x}$ = s = CI =
• $\overline{x}$ = s = CI =
• $\overline{x}$ = s = CI =
• $\overline{x}$ = s = CI =
• $\overline{x}$ = s = CI =
• $\overline{x}$ = s = CI =
• $\overline{x}$ = s = CI =
• $\overline{x}$ = s = CI =

## Discussion questions

1. The actual population mean for the 100 heights given above is μ = 63.3. Using the samples above, for how many intervals does the value of μ lie between the endpoints of the confidence interval? .

2. What percentage of the total number of confidence intervals generated contain the mean μ?

3. Is the percent of confidence intervals that contain the population mean μ close to 90%?

4. Suppose we had generated 100 confidence intervals. What do you think would happen to the percent of confidence intervals that contained the population mean? Use 2 – 3 complete sentences.

5. When we construct a 90% confidence interval, we say that we are 90% confident that the true population mean lies within the confidence interval. Using complete sentences, explain what we mean by this phrase in terms a non-statistician would understand.

6. Some students think that a 90% confidence interval contains 90% of the data. Use the first confidence interval calculated and count how many of the 100 data values lie within that confidence interval? What percent is this? Is this percent close to 90%? Using 3 – 4 sentences to explain why it should or should not be close to 90%.

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