Question

You are testing a treatment for a new virus. Effectiveness is judged by the percent reduction in symptoms after two weeks.It is known that if left untreated, symptoms will reduce on their own by 0.185 (18.5%) with a standard deviation of 0.123. Three trials were run simultaneously.Trial 1 involved giving the participants a sugar pill. Patients in Trial 2 were given Agent A. Patients in Trial 3 were given Agent B. Results showing the amount of symptom reduction for the various trials are summarized in the table to the left. Note that this is NOT a paired t-test.Patient 1 just means the first patient to be given the treatment in each trial. Patient 1 is a different person in each trial.

1) At the 80%, 90% and 95% confidence levels (alpha = 0.2, 0.1 and 0.05) compare Agent A, Agent B and the Sugar Pill results to the population symptom reduction. Use a one-tail hypothesis test.

	Percent Reduction in Symptoms after 2 weeks
		Sugar Pill		Agent A		Agent B
	Person 1	0.15		0.8		0.25
	Person 2	0.18		0.02		0.31
	Person 3	0.05		0.18		0.44
	Person 4	0.35		0.9		0.6
	Person 5	0.22		0.12		0.08
	Person 6	0.22		0.11		0.12
	Person 7	0.2		0.33		0.33
	Person 8	0.15		1		0.5
	Person 9	0.45		0.07		0.31
	Person 10	0.1		0.15		0.18
	Person 11	0.29		0.08		0.2
	Person 12	0.08		0.02		0.33
	Person 13	0.3		0.16		0.02
	Person 14	0.21		0.09		0.17
	Person 15	0.13		0.77		0.38
	Person 16	0.4		0.85		0.46
	Person 17	0.31		0.03		0.23
	Person 18	0.02		0.06		0.31
	Person 19	0.09		0.18		0.28
	Person 20	0.17		0.22		0.09
	average	0.204		0.307		0.280
	std dev	0.117		0.340		0.150
	VAR	0.0136		0.1159		0.0225

	Q1	Ho: muX <= 0.185          (where X = Sugar Pill, Agent A or Agent B)
		Sugar Pill vs. Populatoin			Agent A vs Population			Agent B vs Population
	Alpha	Test stat	Critical value	Conclusion	Test stat	Critical value	Conclusion	Test stat	Critical value	Conclusion
	0.2
	0.1
	0.05

Answer 1

Ans ) for sugar pill vs population
we have

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	0.185
Level of Significance	0.2
Sample Size	20
Sample Mean	0.2035
Sample Standard Deviation	0.116631448
Intermediate Calculations
Standard Error of the Mean	0.0261
Degrees of Freedom	19
t Test Statistic	0.7094
Upper-Tail Test
Upper Critical Value	0.8610
p-Value	0.2434
Do not reject the null hypothesis

for Agent A vs population

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	0.185
Level of Significance	0.2
Sample Size	20
Sample Mean	0.307
Sample Standard Deviation	0.340419246
Intermediate Calculations
Standard Error of the Mean	0.0761
Degrees of Freedom	19
t Test Statistic	1.6027
Upper-Tail Test
Upper Critical Value	0.8610
p-Value	0.0627
Reject the null hypothesis

for Agent B vs population

we have

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	0.185
Level of Significance	0.2
Sample Size	20
Sample Mean	0.2795
Sample Standard Deviation	0.150034207
Intermediate Calculations
Standard Error of the Mean	0.0335
Degrees of Freedom	19
t Test Statistic	2.8168
Upper-Tail Test
Upper Critical Value	0.8610
p-Value	0.0055
Reject the null hypothesis

	Sugar Pill vs. Populatoin			Agent A vs Population			Agent B vs population
Alpha	Test stat	Critical value	Conclusion	Test stat	Critical value	Conclusion	Test stat	Critical value	Conclusion
0.2	0.7094	0.861	Fail to Reject Ho	1.6027	0.861	Reject Ho	2.8168	0.861	Reject Ho
0.1	0.7094	1.3277	Fail to Reject Ho	1.6027	1.3277	Reject Ho	2.8168	1.3277	Reject Ho
0.05	0.7094	1.7291	Fail to Reject Ho	1.6027	1.7291	Fail to Reject Ho	2.8168	1.7291	Reject Ho