Question

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	70	20	15	105
Tablet B	60	10	20	90
Placebo	40	35	25	100
Total	170	65	60	295

Contingency Table: Headache 6
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 3x3 table of expected outcomes (round values to 3 decimal places).

	Headache Disappeared	Headache Improved	No Change
Tablet A		23.136
Tablet B			18.305
Placebo	57.627

Results:
Calculate the  test statistic (use two decimal places).

State the p-value (round answer to the nearest hundredth of a percent - i.e. 1.53%)

p-value =

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.)

Answer 1

The Expected value data are in the table below. Each Cell = Row total * Column Total/N. N = 295

The degrees of freedom, df = (r – 1) * (c -1) = (3 - 1) * (3 - 1) = 4

Expected
	Disappeared	Improved	No Change	Total
Transportation	60.509	23.136	21.356	105
Information	51.864	19.831	18.305	90
Financial	57.627	22.034	20.339	100
Total	170	65	60	295

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The Test Statistic: The table below gives the calculation of .

#	Observed	Expected	(O-E)	(O-E)2	(O-E)2/E
1	70	60.509	9.4915	90.08857	1.4889
2	60	51.864	8.1356	66.18799	1.2762
3	40	57.627	-17.6271	310.7147	5.3918
4	20	23.136	-3.1356	9.831987	0.4250
5	10	19.831	-9.8305	96.63873	4.8732
6	35	22.034	12.9661	168.1197	7.6300
7	15	21.356	-6.3559	40.39746	1.8916
8	20	18.305	1.6949	2.872686	0.1569
9	25	20.339	4.661	21.72492	1.0681
Total					24.202

test = 24.20

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The p value: The p value at test = 24.2, df = 4; P value = 0.0001

______________________

The Conclusion: We have sufficient evidence to to support the claim that patient headache status is dependent on which headache relief tablet was used (p < 0.01)

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