Question

1. (7) A new drug is developed to treat headache, and we want to compare its performance with an existing drug. The performance measure here is the time from taking the drug to people start to feel better. A random sample of volunteers were collected, in one occasion of headache, these people use one of the drug, and then in another occasion of headache (there is a long time between occasions), these volunteers use the other drug. Assuming all variables are Normal, use the SPSS outputs to answer questions.

                                                                

      Paired Samples Test

	Paired Differences mean	Std. Dev.	Std. Error	t	df	Sig. (2-tailed)
New– old	.4	.750	.250	1.98	8	.058

Independent Samples Test

Group Statistics
	drug	N	Mean	Std. Deviation	Std. Error Mean
time	old	22	3.09855	.416654	.088831
	new	24	3.31996	.334813	.068343

Independent Samples Test

	Levene's Test for Equality of Variances		t-test for Equality of Means
	F	Sig.	t	df	Sig. (2-tailed)
Equal variances assumed	.043	.0388	-1.863	28	.0794
Equal variances not assumed			-1.680	24.9	.0888

1.            Which t test will you use?

          

2.           What are the hypotheses if you intend to show that the new drug is better?

3. What is the t and P-value for this test?

4. Will H_o be rejected at 5% level of significance?

5. What is your final conclusion?

Answer 1

Solution-a:

we use paired t test as the subjects are same for old and new

          What are the hypotheses if you intend to show that the new drug is better?

Ho:Mu1-Mu2=0

Ha:Mu1-Mu2>0

Mu1=avergae time for new drug

Mu2=avergae time for old drug

What is the t and P-value for this test?

t=1.98

p value for two tail given=0.058

we need p value for one tail=0.058/2=0.029

Will H_o be rejected at 5% level of significance?

alpha=0.05

p=0.029

p<0.05

Reject Ho

Accept Ha

What is your final conclusion?

There is suffcient statistical evidence at 5% level of signficance to conclude that the new drug is better compared to old drug.