Post on 14-Dec-2015
Hypothesis Test for Proportions
Section 10.3
One Sample
Remember: Properties of Sampling Distribution of Proportions
Approximately Normal if
pp
p
pq
n
5
5
np
nq
Test Statistic
pt. estimate - parameter
st. errorstatistic - parameter
st. dev.
z
z
p pz
pqn
Conditions
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
: 0.15
: 0.15o
A
H p
H p
Assumptions:
(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.
0.15(0.85)200
0.19 0.151.58
pqn
p pz
2(0.057) 0.114p val
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 P arameter H ypotheses A ssumptions N ame the test T est statistic O btain p-value M ake decision S tate conclusions in context
If the significance level is not stated – use 0.05.
Reject Ho
There is sufficient evidence to support the claim that …..
Fail to Reject Ho
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.
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.