Authentic Learning Task (ALT) #5: Testing the Light

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ALT #5: Testing the Light

Overview

In this Authentic Learning Task (ALT), you are introduced to hypothesis testing. You inspect shipments of light bulbs sent to a company for resale to uncover whether or not the bulbs meet the manufacturer's claim of 750 hours of use. If there is strong enough evidence that any shipment does not, it will be sent back.

You use Excel to simulate four shipments of bulbs. You take your samples from the Excel spreadsheet and run a t-test on each to make your determination.

After completing this ALT, you should be able to demonstrate the following competency:

  • Analyze variability in a process using hypothesis testing
    (Comp. 5) .

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

In this activity we address the question: Does the shipment of light bulbs meet our life requirement of 750 hours? This problem question is of the general form: “Is there a significant difference between (among) the sample means?

Click here to access a Decision Tree to aid in the selection of the proper test. In this case we will be sampling from an incoming lot of materials and then perform a life test to determine if the lot meets the requirement.

In the past, you may have worked with individual values to compare to a specification limit. If the exercise had asked "Do the individual bulbs meet a minimum specification of 750 hours?", it would have been a significantly tougher requirement than specifying that the lot average must meet the minimum of 750 hours.

Hypothesis testing - Use of the t and z distribution
The Z values for the normal distribution assume large sample sizes
(> 30 samples). In many problems we are faced with a sample that is smaller than 30. In order to compensate for the smaller sample W. Gossett created a new distribution called the “Student t-test” in the early 1900's. Gossett’s employer* had regulations concerning trade secrets that prevented him from publishing his discovery, but in light of the importance of the t distribution, Gossett was allowed to publish under the pseudonym "Student".

In this activity, you test an incoming shipment of fifteen light bulbs to determine their life in hours. The specification requires that we have an average minimum life of 750 hours.

Use the Data Analysis Package in Excel or Use StatCrunch to
assist you.

Click here to view an example problem.

Self Assessment

Click here to complete the self assessment. Answers to the self assessment can be found here.

Activity

In your team, perform the following steps to complete the activity:

  1. Collaborate on setting up the hypothesis test and agree on a method of finding a representative sample of 15 bulbs from each shipment.
  2. Review Information Sheet: Running a T-Test.
  3. Calculate the necessary statistics and run a t-test.
  4. Refer to Data Sheet: Just the Facts and answer Questions 1 and 2, record the results from each test in the table in Question 3, and complete Question 4.
  5. Complete the table in Question 5 on Data Sheet: Just the Facts.
  6. Review Type I and Type II error from Information Sheet: Running a T-Test.
  7. Answer Question 6 on Data Sheet: Just the Facts.
  8. Answer Question 7 on Data Sheet: Just the Facts.
  9. Read and discuss Information Sheet: Hypotheses, Null and Alternative and Information Sheet: Hypothesis
    on Trial.

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 #6: Colors in the Bag.

Assessment
Your facilitator may use Assessment Sheet: Testing the Light to evaluate your results from the activity and your posting to the Discussion Board.

Go to next ALT

Probability, Sampling, and Hypothesis Testing Home Page