1. WARM – UP

2. Part (b)

3. Chapter 21 – More about Tests
Power – The Probability that a significance test will correctly reject a false H0. “Doing the right thing.”
1. Power = 1 – β (Type II Prob.)
2. Increasing sample size, n, decrease Type II errors and
consequently increases the Power of the test.
3. Increasing α increases the Power of the test.
Decision based on sample
Reject H0
Fail to Reject H0
H0 is True
H0 is False
Correct Decision
POWER
Type I Error
Type II Error
Correct Decision

4. Ch. 21 – Test and Confidence Intervals.
The Gallup Poll asked a random sample of 1785 adults, “Did you attend church or synagogue in the last 7 days?” Of the respondents, 750 said “Yes.”
a.) Find the 95% Confidence Interval for the % of all adults who attended church or synagogue during the past week. (Follow all steps)
b.) Do the results provide good evidence that less than half of the population attend church or synagogue? Give supporting evidence? (Follow all steps)

5. The Gallup Poll asked a random sample of 1785 adults, “Did you attend church or synagogue in the last 7 days?” Of the respondents, 750 said “Yes.”
a.) Find the 95% Confidence Interval for the % of all adults who attended church or synagogue during the past week. (Follow all steps)
One Proportion
Z– Conf. Int.
SRS – Stated
Appr. Normal: 1785(0.420)=749.7 ≥ (1 – 0.420)= ≥ 10
Population of Adults ≥ 10(1785)
We can be 95% confident that the true proportion of adults who attended church or synagogue in the past 7 days is between 39.7% and 44.3%.

6. We can be 95% confident that the true proportion of adults who attended church or synagogue in the past 7 days is between 39.7% and 44.3%.
b.) Of 1785, 750 said “Yes.” Do the results provide good evidence that less than half of the population attend church or synagogue? Give supporting evidence? (Follow all steps)
p = The true proportion of adults that attend church or synagogue in the past 7 days. 1. 2.
H0: p = 0.50 Ha: p < 0.50 3.
One Proportion
z – Test 4.
SRS: Stated
Appr. Normal: 1785(0.50)= ≥ (1 – 0.50) = 892.5≥ 10
Population of Adults ≥ 10(1785) 5.
Since the P-Value is less than α = we REJECT H0. There is sufficient evidence that The % of adults attending church or synagogue is less than 50%. 6.

7. Confidence Intervals and Hypothesis Tests
When the alternative is two-sided, the critical value splits  equally into two tails: C%
If the test “REJECTS H0” at the α-level, then the parameter will NOT be in the C = (1 – α)% Confidence interval.
If the test “FAILS to REJECTS H0” at the α-level, then the parameter WILL be in the C = (1 – α)% Confidence interval.

8. Definition of Confidence Level: Definition of Central Limit Theorem:
Thursday’s Quiz
Definition P-Value:
Definition of Confidence Level:
Definition of Central Limit Theorem:
Proportion Assumptions/Conditions:
Decision/Conclusions based on p-value:
Definition of Type I and II Errors and Power:
Construct and Interpret Confidence Interval
Perform Significance Test.
Probability of obtaining statistics or ones more extreme, given H0 is true. {context}
In Repeating Sampling C% of the constructed intervals will contain the True Parameter.
A large random sample will produce an approximately normal distribution. {context}

9. Homework- Page 491: 1,2,5a,6a, 8,9

12. Chapter 21 – More about Tests
P-value ≤ 0.05
-Reject H0
-Evidence supporting Ha
P-value > 0.05
- Fail to Reject H0
- Insufficient Evidence
supporting Ha
Decision Conclusion

13. H0 : p = 0.40 (p=The proportion of female executives.)
HA : p < 0.40

14. H0 : p = 0.40 (The proportion of female executives.)
HA : p < 0.40
One Proportion
z – Test
Randomization condition: Executives were not chosen randomly,
10% condition: Population of employees at the company > 10(43)
Success/Failure condition: np= (43)(0.40) = 17.2 and n(1 – p) = (43)(0.60) = 25.8 are both >10, so the sample is large enough.
The conditions have not all been satisfied, so a Normal model may or may not be valid, so we continue with Caution.

15. Since the P-value = 0. 0955 is high (p>0
Since the P-value = is high (p>0.05), we fail to reject the H0. There is little evidence to suggest proportion of female executives is any different from the overall proportion of 40% female employees at the company.

16. You can also reject using just the z-score.
– Any z-score larger in magnitude than a particular critical value leads us to reject H0.
Any z-score smaller in magnitude than a particular critical value leads us to fail to reject H0. 
1-sided
2-sided
0.01
2.28
2.575
0.05
1.645
1.96
0.10
1.282
2.28
1.282
1.645