1. Hypothesis Test for Proportions
Section 10.3
One Sample

2. Remember: Properties of Sampling Distribution of Proportions
Approximately Normal if

3. Test Statistic

4. Conditions

5. p=true proportion of seniors who dropout
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:
(1) SRS
(2) Approximately normal since np=200(.15)= 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.
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?

6. 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

7. If the significance level is not stated – use 0.05.

8. Reject Ho
There is sufficient evidence to support the claim that …..

9. Fail to Reject Ho
There is insufficient evidence to support the claim that ….

10. 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

11. Experts claim that 10% of murders are committed by women
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.

12. Experts claim that 10% of murders are committed by women
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.

13. 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.

14. 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?

15. 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.