Two-Sample Hypothesis Testing

1
Two-Sample Hypothesis Testing

• Example
• A professor has designed an experiment to test
  the effect of reading the textbook before
  attempting to complete a homework assignment.
  Four students who read the textbook before
  attempting the homework recorded the following
  times (in hours) to complete the assignment
• 3.1, 2.8, 0.5, 1.9 hours
• Five students who did not read the textbook
  before attempting the homework recorded the
  following times to complete the assignment
• 0.9, 1.4, 2.1, 5.3, 4.6 hours

2
Two-Sample Hypothesis Testing

• Define the difference in the two means as
• µ1 - µ2 d0
• What are the Hypotheses?
• H0 _______________
• H1 _______________
• or
• H1 _______________
• or
• H1 _______________

3
Our Example

• Reading
• n1 4 x1 2.075 s12 1.363
• No reading
• n2 5 x2 2.860 s22 3.883
• If we assume the population variances are
  equal, we can calculate sp2 and conduct a
  __________.
• __________________

4
Your turn

• Lower-tail test ((µ1 - µ2 lt 0)
• Fixed a approach (Approach 1) at a 0.05
  level.
• p-value approach (Approach 2)
• Upper-tail test (µ2 µ1 gt 0)
• Fixed a approach at a 0.05 level.
• p-value approach
• Two-tailed test (µ1 - µ2 ? 0)
• Fixed a approach at a 0.05 level.
• p-value approach
• Recall ?

5
Lower-tail test ((µ1 - µ2 lt 0)

• Draw the picture
• Solution
• Decision
• Conclusion

6
Upper-tail test (µ2 µ1 gt 0)

• Draw the picture
• Solution
• Decision
• Conclusion

7
Two-tailed test (µ1 - µ2 ? 0)

• Draw the picture
• Solution
• Decision
• Conclusion

8
Another Example

• Suppose we want to test the difference in
  carbohydrate content between two low-carb
  meals. Random samples of the two meals are tested
  in the lab and the carbohydrate content per
  serving (in grams) is recorded, with the
  following results
• n1 15 x1 27.2 s12 11
• n2 10 x2 23.9 s22 23
• tcalc ______________________
• ? ________________ (using equation in table
  10.2)

9
Example (cont.)

• What are our options for hypotheses?
• At an a level of 0.05,
• One-tailed test, t0.05, 15 ________
• Two-tailed test, t0.025, 15 ________
• How are our conclusions affected?