1. AP STATISTICS REVIEW INFERENCE

2. Statistical Inference
Drawing conclusions (“to infer”) about a population based upon data from a sample.
Two types of inference:
Confidence intervals
Significance tests
USB Documents\AP STATISTICS\quick guide to inference.pdf

3. Confidence Intervals Confidence intervals estimate the true value
of the parameter where the parameter is the
true mean , true proportion p, or true slope .

4. Confidence Intervals 1-sample t-interval for 2-sample t-interval for
Matched-pairs t-interval
1-proportion z-interval for p
2-proportion z-interval for p1 - p2
t-interval for slope

5. Confidence Intervals P = Parameters A = Assumptions (conditions) C S
= Calculate interval
= State a conclusion

6. Interpret the confidence level:
C% of all intervals produced using this method
will capture the true mean (difference in means), or proportion (difference in proportions), or slope.
(Describe the parameter in context!)

7. Interpret the confidence interval:
I am C% confident that the true parameter (insert context) is between ___ and ___ (insert units), based on this sample.

8. (2000) Question 6
A random sample of 400 married couples was selected from a large population of married couples.
Heights of married men are approximately normally distributed with a mean 70 inches and standard deviation 3 inches.
Heights of married women are approximately normally distributed with mean 65 inches and standard deviation 2.5 inches.
There were 20 couples in which the wife was taller than her husband, and there were 380 couples in which the wife was shorter than her husband.
Find a 95 percent confidence interval for the proportion of married
couples in the population for which the wife is taller than her husband. Interpret your interval in the context of this question.

9. Solution (2000 – Question 6, part a)
Parameter, Assumptions, Test Name (or formula):
p = true proportion of married couples in which the
wife is taller than her husband
Assumption: large sample size since
1-proportion z-interval for p

10. Solution (2000 – Question 6, part a)
Calculations:

11. Solution (2000 – Question 6, part a)
Interpret the interval:
I am 95% confident that the true proportion of couples in which the wife is taller than her husband is between .028 and .071, based on this sample.
USB Documents\AP STATISTICS\AP Stats\correct & incorrect ways to explain CI.doc

12. Significance Tests H = Hypothesis (define parameters!) A
= Assumptions (conditions)
= Test name or formula
= State a conclusion

13. Significance Tests
Significance tests provide evidence for some claim using sample data.
test statistic =
estimated value – hypothesized value
standard error of the estimate

14. Significance Tests 1-sample t-test for 2-sample t-test for
Matched pairs t-test
1-proportion z-test for p
2-proportion z-test for p1 – p2
Chi-square goodness-of-fit test
Chi-square test for homogeneity or independence/association
t-test for slope 

15. What is the P-value?
The P-value is the probability of getting an observation as extreme or even more extreme by chance alone, assuming that the null hypothesis is true.
If the P-value is small (< alpha), then we reject Ho and accept Ha. (Results are statistically significant)
If the P-value is large (> alpha), then we fail to reject Ho and fail to accept Ha. (Results are not statistically significant)

16. Know your inference procedures
Helpful web site:

17. (2000) Question 4

18. Solution (2000) Question 4

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24. Scoring (2000) Question 4

25. Scoring (2000) Question 4

26. (2003) Question 5

27. Solution (2003) Question 5

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31. Scoring (2003) Question 5

32. Type I, Type II Errors & Power
Type I Error ()
Ho is true, but we reject Ho (& support Ha)
Type II Error ()
Ho is false, but we fail to reject Ho (& fail to
support Ha)
Power (1- )
the probability of correctly rejecting Ho

33. Type I, Type II Errors & Power

34. How to increase power: Increase alpha (level of significance)
Increase the sample size, n
Decrease variability
Increase the magnitude of the effect (the difference in the hypothesized value of a parameter & its true value

35. (2003) Question 2

36. Solution (2003) Question 2

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39. Scoring (2003) Question 2

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41. Scoring (2003) Question 2

42. Scoring (2003) Question 2

43. Good Luck!