AP Statistics Section 11.4 B

A significance test makes a Type I error when

___________________________________ P(Type 1 error ) = ___

A significance test makes a Type II error when

__________________________________.

e.really tru is H theand H rejectsit 00

ereally tru is H theand H rejects tofailsit a0

0Hreject tofail

Type II errors are always computed at a particular value for .

Calculating the probability of a Type II error by hand is possible but unpleasant. It’s better to let

technology do the work for you.

You will not be expected to find P(Type II error) on the AP exam.

aH

If the probability of a Type II error for a particular Ha is high, this means that the test is not sensitive (or tuned-in) enough to regularly detect that Ha.

power

sensitive more

-1 trueis H when H

rejectingnot ofy Probabilit

a0

EXAMPLE: If you learned that the power of a .05 significance test in the paramedic response time

example against the alternative value was .81, explain what that would mean in this setting.

minutes. 6.4actually is timeresponse paramedic true

when the6.7:H reject the test willcesignifican

that thechance 81%an is theremeans .81 ofpower A

0

Calculations of p-values and calculations of power both tell us what would happen if

the test were repeated many times.

A p-value tells us what would happen supposing that the ___________, while

power describes what would happen supposing a particular __________.

trueis 0H

trueis aH

When planning a study that will include a significance test, a careful user of statistics

decides what alternative values of the parameter the test should detect and

checks that the power is adequate. The power depends on which particular

parameter value in we are interested in. To calculate power, we must fix an so that there is a fixed rule for rejecting .

aH

0H

Increasing the Power

High power is always desirable. Along with ____ confidence

intervals and ____ significance tests, ____ power is becoming a

standard.

%95%5

%80

The best advice for maximizing the power of a test is to choose as high an___level as you are willing to risk AND

as large a sample size as you can afford.

error I Type a of

y probabilit theincrease