Presentation Transcript
Slide 1:Page 1 Hypothesis Tests Hypothesis
Testing
1
-
Basic
Ideas
Slide 2:Page 2 Your friend proposes a series of bets using a coin. Basic Hypothesis Testing She flips… You figure the probability of a head or a tail is
0.50 so there isn’t much of a risk. Heads. You lose. She flips again… 2 Heads. Lucky!. And again… 3 Heads. Very lucky. And again… 4 Heads? Getting suspicious here. And again… 5 Heads!!! OK. That’s it. Something’s wrong here. Turn the coin over… Look at it this way. Hey! Heads on both sides. For only $5, your friend has taught you basic Hypothesis Testing. She chooses HEADs. You agree to bet $1 on each flip.
Slide 3:Page 3 Basic Hypothesis Testing You went into this arrangement believing that the
coin was fair. In 5 tosses, you would expect a fair coin to come
up heads 2 or 3 times, P( 5H out of 5 ) = (0.5)5 = 0.031 0 1 2 3 4 5
No. of Heads but the probability of 5 heads in 5 tosses is only If a fair coin were tossed 5 times, the
outcome probabilities would be as shown below. This is so improbable that you would sooner reject
your original hypothesis that the coin was fair
than believe that such a rare outcome could occur. THAT WAS A BASIC HYPOTHESIS TEST. ok maybe 1 or 4 times,
Slide 4:Page 4 Basic Hypothesis Testing We need to consider one important idea. In life, whenever we make a decision, there is
ALWAYS a probability that we are WRONG. because even
though the probability was small, p=0.031, it was
possible for a fair coin to have produced 5 heads
in a row. In this hypothesis test, when we rejected the
fair coin (Null) hypothesis, we knew that
there was a 0.031 probability that we were
making the wrong decision . . . Wrongly rejecting the null hypothesis is called a Here, it was p=0.031. Type I error and the probability of making that error is called the p-value.