STA258
Week 7 Practicum
1
Decisions Errors in Tests
2
Type I Error
• Ho is true, but sampling error in the data leads you to reject Ho,
you’ve made a Type I error.
• When Ho is true, a Type I error occurs if Ho is rejected.
• The probability of a Type I error is the significance level of the
hypothesis test. The probability of a Type I error is denoted by
Type II Error
• Ho is false, but sampling error in the data does not leads you to
reject Ho, you’ve made a Type II error.
• When Ho is false, a Type II error occurs if Ho is not rejected.
• The probability of making a type II error is denoted by
Example of Decisions Errors in Tests
3
Jury Trial:
Ho: Innocent verses Ha: Guilty
• Type I error: Reject Ho when it is true.
A Type I error occurs if the jury convicts an innocent .
• Type II error: Fail to reject Ho (“Accept Ho”) when it is false.
A Type II error occurs if the jury fails to convict a guilty person.
Lobster Trap Placement
An observational study of teams fishing of the red lobster in Baja California Sur,
Mexico, was conducted and the results published in Bulletin of Marine Science
(Apr. 2010). One of the variables of interest was the average distance separating trap
– called trap spacing – deployed by the same team of fishermen. Trap spacing
measurement in meters for a sample of seven teams of red spiny lobster fishermen
are shown in the accompanying table.
Let represent the average of the trap spacing measurements for the population of
the red spiny lobster fishermen fishing in Baja California Sur, Mexico.
4
5Suppose you want to determine if the true value of differs from 95 meters.
: = 95 : ≠ 95
∗= -1.1705, df = 6 , p-value = 0.2862 > = 0.05.
We cannot reject : = . We cannot conclude : ≠
We have no evidence to conclude that the mean trap spacing measurements for the population of the red spiny lobster
fishermen fishing in Baja California Sur, Mexico, differs from 95 meters.
We could be making a Type II error.
Statistical Power
Statistical power is the probability of correctly rejecting Ho.
• If T is close to o power will be low
• If T is far from o power will be high
6
( ) 1 ( ) (reject Ho|Ho false ) T T TP      = = − = =
7
8
9Alpha = 0.05 = P(reject Ho | Ho is true)
P(Z < -1.645) = 0.05 (this is the rejection region)
Z critical value is -1.645
Power = P(reject Ho | Ho is false)
= P(
ത−225
7
40
< -1.645 | = 223)
= P( ത < 223.1793186| = 223)
= <
223.17931−223
7
40
= P(Z < 0.1620)
≅ 0.564
10
11
12
13
14
15