A pharmacologist decided to test two common headache-tablets for
their effectiveness: Tablet A 500mg and Tablet B 20 mg. The
experiment was conducted as follows: A random patient that walked
into the clinic and complained of a headache was given either
tablet A, tablet B, or a placebo. After swallowing the tablet the
patient was asked to stay in the clinic for an hour and afterwards
to report whether the headache had disappeared, improved, or if the
tablet had no effect (i.e. no improvement or even a worsening of
the headache intensity). Use a 1% level of significance to test the
claim that headache status is independent of headache relief tablet
used.
|
Headache Disappeared |
Headache Improved |
No Change |
Total |
|
|
Tablet A |
65 |
20 |
15 |
100 |
|
Tablet B |
60 |
10 |
20 |
90 |
|
Placebo |
50 |
32 |
23 |
105 |
|
Total |
175 |
62 |
58 |
295 |
Contingency Table: Headache 9
Hypotheses:
H0: Headache status is independent of headache
relief tablet used.
H1: Headache status is dependent on headache
relief tablet used.
Expected Values:
Complete the 3×3 table of expected outcomes (round values to 3
decimal places).
|
|
Headache Disappeared |
Headache Improved |
No Change |
|
Tablet A |
21.017 |
||
|
Tablet B |
17.695 |
||
|
Placebo |
62.288 |
Results:
Calculate the test statistic (use two decimal
places).
State the critical value from Table 3 in the textbook
(page 242).
Conclusion:
We sufficient evidence to support the claim that patient
headache status is dependent on which headache relief tablet was
used (p 0.01).
(Use “have†or “lack†for the first blank and “<†or “>†for
the second blank.)
