Transcript Understanding Basic Statistics

Chapter 10: Inferences About
Differences
10.1 – Tests Involving Paired Differences
(Dependent Samples)
10.2 – Inferences About the Difference of Two
Means (µ1 – µ2)
10.3 – Inferences About the Difference of Two
Proportions (p1 – p2)
Focus Problem
“The Trouble with Wood Ducks”
• Read page 415-416 in text book
– Yes, it may be used in a HW problem!
10.1 – Tests Involving Paired
Differences (Dependent Samples)
Two samples are dependent if each data value in one
sample can be paired with a corresponding data value in
the other sample.
Examples: twins; plant growth on plots of land matched
for soil type, moisture, or sun; matched inventories
(selling more of one item); natural existences....left foot
size larger than right; before/after effects; increases of
matched data; etc
Guided Exercise #1
• As whole group, turn to page 417
– Look-over answers
– Whole group clarification
Testing
Consider a random sample of n data pairs. Suppose the
differences d̅ between the first and second members of
each data pair are approximately normally distributed
with population mean μd
𝑡=
𝑑− µ𝑑
𝑠𝑑
𝑛
with d.f. = n – 1
• sd = sample standard deviation of the differences d
• n = number of data pairs
• μd = 0 as specified in Ho
How to Test Paired Differences Using
the Student’s t Distribution
Same as before…
1. Null Hypothesis, alternative hypothesis, level
of significance
2. T score
3. P-value (left, right or two tailed)
4. Reject or not reject null hypothesis
5. Conclude using context.
Guided Exercise #2
• As whole group, turn to page 421
– Look-over answers
– Whole group clarification
Test conclusions based on critical
values
• Right tail: if sample test statistic ≥ critical value,
reject Ho
• Left tail: if sample test statistic ≤ critical value,
reject Ho
• Two Tailed: if the sample test statistic lies beyond
the critical values, reject Ho
– That is, ≤ negative critical value or ≥ positive critical
value.
• Otherwise do not reject Ho
Checkpoint
Tator Tots
Homework
• Read Pages 414-425
– Take notes on what we have not covered
• Do Problems
– Page 425-429 (1-12) ALL
• Check odds in back of book
• Read and preload 10.2 information
– Notes/vocab