| Overview
In this Authentic Learning Task (ALT), you look at a decision statement
and the corresponding level of significance. These factors are at
work every day in business and industry whenever a company needs
to test a population to certify that it meets a given value.
You measure the vertical bounce height of golf balls dropped from
the same height. You test 40 golf balls to produce a normal distribution
with average and standard deviation. You separate the quality golf
balls from the economy ones on the basis of their bounce height
and discover what percentage of balls will test at the
economy level. You use the distribution (mean and standard deviation)
to make decisions about separating the balls into two groups, economy
and quality.
After completing this ALT, you should be able to demonstrate the
following competency:
- Using normal distribution, analyze error and determine a significance
level based upon risk with which the user is comfortable (Comp.
4).
Materials and Equipment
No materials or equipment are needed for this ALT.
Safety and Disposal
No special safety or disposal procedures are required.
Pre-Activity
Significance Levels and the Law of Large Numbers
In this activity the use of many repeated independent
trials you will test the premise of the law of large numbers by
observing whether or not the relative frequency in which an event
occurs tends toward the expected probability of the event and then
determine the descriptive statistics of the collected data. Using
this collected data then determine the value that divides the lower
25%, classified as economy, from the upper 75%, classified as quality.
The first learning object, Reasoning
of a Statistical Test, provides you a simulation that illustrates
the concept of convergence.
Using the Online
Statistical Calculator (free) that operates much like Excel
will provide us with an example of how to complete this task.
Step 1: Collect sample drops. From twenty-five
“sample” drops, the following histogram and descriptive
statistics were exported from Statcrunch.
Step 2: Determine the corresponding Z value for
a lower 25% tail from the standard Normal Table. In this case using
the Normal
table, we estimate in the table the Z value for 25% or .25 as
Z lower = -0.675 since it is the “bottom” 25%.
Step 3: Use that Z value to calculate the corresponding
bounce height value. Using the formula Z = (Lower Limit - Mean)/
Std. Dev.
-0.675 = (LL – 22.95)/6.013
The Lower Limit = 18.9. This defines the upper boundary of the
bottom 25% and is considered our level of significance.
Self Assessment
For practice determine the level of significance for 1%, 5%,10%
and 50% for the bounce height data set.
Click here
for the worked answers to the problem.
Activity
In your team, perform the following steps to complete the activity:
- Complete Instruction Sheet: How High?
- Complete Data Sheet: Making the Cut.
Post-Activity
Your team should now post all of its results from the activity
to the Discussion Board.
Assignment
There are no instructions to prepare for ALT #5: Testing the Light.
Assessment
Your facilitator may use Assessment Sheet: How High? to evaluate
your results from the activity and your posting to the Discussion
Board.
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