### Two-Sample Inference Testing

```AP Statistics
Thursday, 10 April 2014
• OBJECTIVE TSW (1) quiz over two-sample
inference and (2) review for tomorrow’s test covering
two-sample inference.
• ASSIGNMENT DUE
– WS Mixed Hypothesis Review #1
• QUIZ: 2-Sample Inference – Means &
Proportions will be given momentarily.
• TEST: Two-Sample Inference is tomorrow.
WS: Two-Sample Inference with Means #1
1)
(32.494, 40.799)
We are 95% confident that the true difference
in mean sugar content between children and
adult cereals is between 32.494% and 40.799%.
2) t = 1.406
p-value = 0.0801
df = 590.049
Fail to reject
3) (–0.2898, 1.7378)
Since 0 is in the interval, there is not evidence
of a difference.
WS: Two-Sample Inference with Means #1
4) t = 2.478
p-value = 0.01509
Fail to reject H0.
5) Type I error
df = 90.486
WS: Two-Sample Inference with Means #2
1)
Normal distribution,
μpu – pe = 16 – 14 = 2 lbs
pu – pe = 0.72/15 + 0.52/15 = 0.2221 lbs
2)
P( (x-barpu – pe) < 1.8) = 0.1839
3)
P(1.5 < (x-barpu – pe) < 2.5) = 0.9756
4)
40th %’ile = 1.9437 lbs
5)
95th %i’le = 2.3653 lbs
QUIZ: 2-Sample Inference
Means & Proportions
Test Topics:
Two-Sample Inference Testing
• Know the pooling pˆ formula.
x1  x2
pˆ 
n1  n2
• Compute confidence intervals for differences in
means.
• Compute confidence intervals for differences in
proportions.
• Know the conditions for using z-tests and t-tests.
Test Topics:
Two-Sample Inference Testing
• Identify Type I and Type II errors.
• State conclusions:
– Confidence intervals: “We are < >% confident that …”
– Hypothesis tests: “p < > , so we reject/fail to reject …”
• Know the formula for calculating a z-test statistic
for hypothesis testing.
 pˆ1  pˆ2 
1
1
pˆ 1  pˆ  

n n
1
2
Test Topics:
Two-Sample Inference Testing
• Know the relationship between power and .
• Compute sample sizes for given confidence
intervals.
• Compute standard error.
• Know the characteristics of a matched-pairs test.
• Perform a full two-sample proportion hypothesis
test.
WS AP Mixed Review: Two-Sample Inference
1.
E
9.
E
2.
B
10.
A
3.
B
11.
D
4.
D
12.
C
5.
C
13.
A
6.
E
14.
C
7.
E
15.
A
8.
D
16.
B
```