1. Inference
Confidence Interval for p

2. Confidence Interval
Plausible values for the unknown population proportion, p.
We have confidence in the process that produced this interval.

3. Inference – Using C.I.
The population proportion, p, could be any of the values in the interval.
Values outside the interval are not plausible values for p.

4. Inference – Hypothesis Test
Propose a value for the population proportion, p.
Does the sample data support this value?

5. Example
A law firm will represent people in a class action lawsuit against a car manufacturer only if it is sure that more than 10% of the cars have a particular defect.

6. Example Population: Cars of a particular make and model.
Parameter: Proportion of this make and model of car that have a particular defect.

7. Example Null Hypothesis Alternative Hypothesis H0: p = 0.10
HA: p > 0.10

8. Example
The law firm contacts 100 car owners at random and finds out that 12 of them have cars that have the defect.
Is this sufficient evidence for the law firm to proceed with the class action law suit?

9. Example
How likely is it to get a sample proportion as extreme as the one we observe when taking a random sample of 100 from a population with p = 0.10?

10. Example Sampling distribution of
Shape approximately normal because 10% condition and success/failure condition are satisfied.
Mean: p = 0.10
Standard Deviation:

11. Draw a Picture

12. Standardize

13. Use Table Z z
0.5
0.7

15. Interpretation
Getting a sample proportion of 0.12 or more will happen about 25% (P-value = 0.25) of the time when taking a random sample of 100 from a population whose population proportion is p = 0.10.

16. Interpretation
Getting a value of the sample proportion of 0.12 is consistent with random sampling from a population with population proportion p = 0.10.
This sample result does not contradict the null hypothesis. The P-value is not small, therefore fail to reject H0.

17. Interpretation
Even though the sample proportion, 0.12, is larger than the hypothesized population proportion, 0.10, it is not large enough for us to believe that the population proportion is greater than 0.10.
There is not convincing evidence.

18. Conclusion
Based on this sample, the law firm should not pursue the class action lawsuit because the population proportion of defective cars could be only 10%.

19. Test of Hypothesis Step 1: State your null and alternative hypotheses.
H0: p = po
HA: p > po

20. Test of Hypothesis Step 2: Check conditions Independence
Random sampling condition
10% condition
Success/Failure condition

21. Test of Hypothesis
Step 3: Calculate the test statistic value and convert it into a P-value.
Use Table Z.

22. Test of Hypothesis Step 4: Use the P-value to reach a decision.
If the P-value is small, then reject Ho.
If the P-value is not small, then fail to reject Ho.

23. Test of Hypothesis
Step 5: State your conclusion in the context of the problem.
What does rejecting, or failing to reject, Ho mean in the context of the problem.

24. Alternatives H0: p = po HA: p < po, P-value = Pr < z

25. Another Example
According to the U.S. census, Story County has 9.7% of its population classified as non-white.
Of 120 people called for jury duty in Story County only 3 are non-white. Is this convincing evidence of under-representation of non-whites?

26. Another Example Step 1: State your null and alternative hypotheses.
H0: p = 0.097
HA: p < 0.097
p is the proportion of non-whites among all people in the jury pool for Story County.

27. Test of Hypothesis Step 2: Check conditions Independence
Random sampling condition
10% condition
Success/Failure condition

28. Test of Hypothesis
Step 3: Calculate the test statistic value and convert it into a P-value.

29. Test of Hypothesis Step 4: Use the P-value to reach a decision.
Because the P-value is small, we should reject Ho

30. Test of Hypothesis
Step 5: State your conclusion in the context of the problem.
This is convincing evidence that non-whites are under-represented in the jury pool.