EC 41; UCLA;
Sample Problems #6A Sections 6.3 and 6.4, (and geometric distribution from 5.2)
revised  numbering and typo for #12 fixed
1)
Suppose someone is convicted of a crime if their guilt is “beyond a shadow of a doubt” = when there is only a 1%
chance they are truly not a criminal.
a) If convicting a true noncriminal is Type I error, what is Type II error?
b) What corresponds to the “power” of a test in this setting?
c) How could the power be increased in this setting?
2)
You must decide which of two possible distributions a random variable X has, p
0
or p
1
. The probabilities for specific
values of X are:
x
0
1
2
3
4
p
0
.05
.05
.1
.2
.6
 The Null Hypothesis is: H
0
: p
0
is correct
p
1
.2
.2
.2
.2
.2
 The Alternate Hypothesis is: H
A
: p
1
is correct
Suppose you follow the rule: accept H
0
if
X = 3 or 4 and reject H
0
otherwise
a) What is the probability of Type I error?
b) What is the probability of Type II error?
c) What is the power of this testing procedure?
3)
You think wages for a group of workers are less than $10 per hour and would like to find evidence to support this
claim. You assume it is impossible for wages of this group to be more than $10, so you use a onetail test. Choose a 5%
level of significance, so the onetail Zcritical will be 1.645. The true standard deviation of wages in this population is $8
per hour. Consider the sample mean from a sample of 16 workers.
Assume we can treat it as a simple random sample
(SRS). Consider a specific alternative value for the true sample mean = $6 per hour.
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 Spring '07
 Guggenberger
 Null hypothesis, Statistical hypothesis testing

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