STAT 301 - Business Statistics
Lecture Review #13 - Introduction to Hypothesis Testing

Review questions:

1) What are the six basic steps in a hypothesis testing problem (as outlined in class)?

2) In what ways is a statistical test of hypotheses like a criminal court trial?

3) Under what circumstances should the null hypothesis be "rejected"? Be "not rejected"?

4) Why do we "not reject" (rather than "accept"), in a hypothesis test?

Computational exercises:

1) Balph Snerdwell* plans to roll a standard, six-sided die 6000 times, counting the number of 1's he gets. He wishes to test whether the die is fair, at least in regard to the number of 1's obtained.

a) State Balph's null and alternative hypotheses, in words and in symbols.

b) Balph gets 1060 1's in those 6000 rolls. Compute a test statistic and a p-value for his test.

c) Give Balph's conclusions, in statistical jargon (reject/don't reject) and in the language of the problem.

2) Willard H. Longcor** conducted some tests of inexpensive and precision-made dice. Two million rolls were made with the precision-made dice, recording on each roll whether an even or odd number appeared. A new die was used after every 20,000 tosses, to guard against imperfections from the wear and tear of being rolled over and over. The same experiment was conducted with inexpensive dice, but Longcor stopped after 1,160,000 rolls. Results from his experiment are given below:

For each type of dice, test the null hypothesis that even and odd numbers are equally likely to be rolled.

* This name is made up, as is the story line.

** I'm NOT making this name up. This really happened. This experiment is reported in Mosteller, Rourke, and Thomas's book Probability with Statistical Applications.

SOLUTIONS:
1) z=2.08, p-value=0.0376, reject null hypothesis
2a) precision dice z=1.27, p-value=0.2040, don't reject null hypothesis
2b) inexpensive dice z=15.6, reject null hypothesis