Transcript Notes on One Sample Proportion Significance Tests

Hypothesis Test for
Proportions
Section 10.3
One Sample
Remember: Properties of Sampling
Distribution of Proportions
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p  p
p 
pq
n
Approximately Normal if
np  5
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nq  5
Test Statistic
pt. estimate - parameter
z
st. error
statistic - parameter
z
st. dev.
p p
z
pq
n
Conditions
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Educators estimate the dropout rate is 15%. Last year 38
seniors from a random sample of 200 seniors withdrew. At a
5% significance level, is there enough evidence to reject the
claim?
p=true proportion of seniors who dropout
Assumptions:
 H o : p  0.15

 H A : p  0.15
(1) SRS
(2) Approximately normal since np=200(.15)=30
and nq=200(.85)=270
(3) 10(200)=2000 {Pop of seniors is at least 2000}
Therefore the large sample Z-test for proportions may be used.
z
p p
pq
n

0.19  0.15
0.15(0.85)
200
 1.58
p  val  2(0.057)  0.114
Fail to reject Ho since p-value >α. There is insufficient evidence to
support the claim that the dropout rate is not 15%. What type of error
might we be making?
PHANTOMS
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P
H
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T
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arameter
ypotheses
ssumptions
ame the test
est statistic
btain p-value
ake decision
tate conclusions in context
If the significance level is not
stated – use 0.05.
Reject Ho
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There is sufficient evidence to support the
claim that …..
Fail to Reject Ho
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There is insufficient evidence to support the
claim that ….
A random sample of 270 CA lawyers revealed 117 who felt
that the ethical standards of most lawyers are high. Does
this provide strong evidence for concluding that fewer than
50% of all CA lawyers feel this way
Experts claim that 10% of murders are committed by women.
Is there evidence to reject the claim if in a sample of 67
murders, 10 were committed by women. Use 0.01
significance.
Experts claim that 10% of murders are committed by women.
Is there evidence to reject the claim if in a sample of 67
murders, 10 were committed by women. Use 0.01
significance.
A study on crime suggests that at least 40% of all arsonists
were under 21 years old. Checking local crime statistics, we
found that 30 out of 80 were under 21. Test at 0.10
significance.
A telephone company representative estimates that 40% of
its customers want call-waiting. To test this hypothesis, she
selected a sample of 100 customers and found that 37% had
call waiting. At a 1% significance, is her estimate
appropriate?
A statistician read that at least 77% of the population oppose
replacing $1 bills with $1 coins. To see if this claim is valid, the
statistician selected a sample of 80 people and found that 55 were
opposed to replacing the $1 bills. Test at 1% level.