Does the width of the confidence interval increase or decrease?

Week 11: Statistics Extra Credit: Confidence Interval
1. Save the File with your Name in it, ie 220_W11EC_TEyster.docx
2. Make sure it is a Word Doc or PDF file to ensure readability.
3. Answer all parts in complete sentences and show all work or explain how you got the values.
Student Learning Outcomes
The student will calculate the 90% confidence interval for the mean length of the provided femurs of patients.
The student will interpret confidence intervals.
The student will determine the effects of changing conditions on the confidence interval.
Data to be used is randomly selected from: femur lengths of patients: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6177158/
Thiesen, D. M., Prange, F., Berger-Groch, J., Ntalos, D., Petersik, A., Hofstätter, B., Rueger, J. M., Klatte, T. O., & Hartel, M. J. (2018). Femoral antecurvation-A 3D CT Analysis of 1232 adult femurs. PloS one, 13(10), e0204961. https://doi.org/10.1371/journal.pone.0204961
The Desmos site below is set up to do all the randomization and calculations for you. Turn off and on the different graphs as needed to see what is happening and to take the individual screenshots for each set.
https://www.desmos.com/calculator/hr8zowh4eg
Click the crossed lines button at the top left a few times to get a new randomized sample from the data set. Don’t forget you can also change colors with the gear icon.
Notice how the Dot Plot & the dotted lines move. The dotted lines are the Lower & Upper limits of the 90% confidence interval, notice how they move each time you click the randomize button. After you have done this a few times, copy the link to your individualized set of data below.
What is the link to your work in Desmos? (Use the button that looks like this: , not the web address)
To export an image of your graph, follow these instructions.
Describe the Data:
(While we don’t know the population standard deviation, we will still use the Normal distribution, since our sample size is greater than 30.)
Export an image of the Dot Plot with the Confidence Interval with the two lines showing.
Then, input the calculated values into the table.
Mean
Standard Deviation
Sample size
α
α/2
Error Bound
Lower Limit ( )
Upper Limit ( )
Some students think that a 90% confidence interval contains 90% of the data.
Using the dot plot from your link, count how many of the data values lie within the confidence interval.
What percent of the data is this?
Is this percent close to 90%?
Discussion Questions:
(For each question, use one to two complete sentences to explain your answer.)
Explain why this percent should or should not be close to 90%.
Explain what this confidence interval means for this particular study.
Compare Confidence Intervals:
(Using the given information, construct a confidence interval for each confidence levels given. Use the Desmos link from your data, adjust ‘α’ appropriately to find the EBM and Intervals.)
Confidence level
EBM/Error Bound
Confidence Interval
80%
( , )
90%
( , )
99%
( , )
Discussion Questions:
(For the last question, use one to two complete sentences to explain your answer.)
What happens to the EBM as the confidence level increases?
(Does it get larger or smaller?)
Choose an item
Does the width of the confidence interval increase or decrease?
Choose an item
In 1-2 quality sentences, explain why this happens.

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