2. YOU HAVE REACHED THE FINAL OBJECTIVE OF THE COURSE
CONGRATULATIONS!!
YOU HAVE REACHED THE FINAL OBJECTIVE OF THE COURSE

3. Section 12.1: Tests of Population Means
AP STAT
Section 12.1: Tests of Population Means
EQ: What is the difference between a one-sided hypothesis test and a two-sided hypothesis test?

4. RECALL: Statistical Inference Part I
Confidence Interval
uses probability to estimate a parameter point (µ or p) within an interval of values

5. RECALL: As sample size increases, margin of error
decreases.

6. Statistical Inference Part II: Significance Tests
– uses probability to compare observed data with a hypothesis whose truth we want to assess
Hypothesis
– numerical value making a statement about a population

7. always “ = “ H0:  = ____ H0 represents a single value Null Hypothesis
– statement being tested
H0 represents a single value
always “ = “
H0:  = ____

8. Ha:  > ____ Ha:  < ____ Alternate Hypothesis
– claim about population for which we are trying to find evidence
Ha represents a range of values
one-sided
Ha:  > ____
Ha:  < ____

9. two-sided
Ha:  ≠ ____

10. p-value
– probability that observed outcome takes a value as extreme or more extreme than that actually observed
Sampling Distribution of a Test Statistic:
test
statistic H0

11. In class p. 745
#1a)
#1b)
#2a)
#2b) 1%

12. --- p-value is as small or smaller than specified α level
Statistically Significant
--- p-value is as small or smaller than specified α level
Larger p-value
 evidence to fail to reject H0; though not enough evidence to conclude Ha
Smaller p-value
evidence to reject H0; enough
evidence to possibly conclude Ha

14. ONLY “FAIL TO REJECT IT”
NEVER “ACCEPT” H0
ONLY “FAIL TO REJECT IT”
Burden of Proof lies on Ha.
H0 is innocent until proven guilty.

15. AP STAT EXAM Scoring Rubric for Significance Testing:

16. See Template for Significance Testing:

20. In class p. 754 Follow Template
#5 (I will give you the summary statistics.)
Parameter of Interest:
µ = mean daily calcium intake for women age 18 to 24 years old
Choice of Test:
1-sample t-test for means

21. Conditions:
SRS --- no reason to assume these women are not representative of population
Independence --- all women age 18 to 24 > 10(38)
Condition met
Normalcy --- sample size large enough, CLT
38 > 30
Condition met

22. Hypothesis: H0 : Ha : µ = 1200 mg µ < 1200 mg
the mean calcium intake is 1200 mg
the mean calcium is less than 1200 mg

23. Calculations:
-3.95

24. Conclusion:
Since the p-value of is less than the significance level α = 0.05, we have evidence to reject the null hypothesis. We have sufficient evidence to possibly conclude that the mean daily caloric intake of calcium is less than 1200 mg for a sample size n = 38 females 18 to 24 years old. Our data are statistically significant.

25. Worksheet: Mean Difference (Matched Pairs)

26. Parameter of Interest: difference.7 .2 .9 .8 .6 .1 .3
Parameter of Interest:
difference
Choice of Test:
t means

27. SRS --- The problem states a SRS of females was taken.
Conditions:
SRS --- The problem states a SRS of females
was taken.
Independence ---
all adult female’s left hand > 10(10)
Condition met
Normalcy --- The problem states the
distribution of finger lengths is normal. .7 .2 .9 .8 .6 .1 .3
Hypothesis:
difference
0 (“there is no difference” )
difference
greater than 0 (“ring finger is longer than index finger”)
> 0

28. Test Statistic:
0.05
Conclusion:
Since the p-value of is less than the significance level
α = 0.05, we have evidence to reject the null hypothesis. We can possibly conclude that the mean difference in length of the ring finger and the length of the index finger on an adult female’s left hand is greater than zero for a sample size n = 10 females.

29. In Class Assignment: p. 754 #8 (a & b)
Use the data on p. 681 to create lists
Before L1 After  L2
Diff of After and Before  L3
Check for Normalcy using boxplot and NPP of L3. Must sketch for condition.
Use the statistics given in #8 to run the test.
HW Practice Worksheet “Inference
for Population Means”