Question

A researcher wants to determine whether or not a given drug has any effect on the score of a human subject performing a task of ESP sensitivity. He randomly assigns his subjects to one of two groups. 900 subjects in group 1 (treatment group) receive the drug. In contrast, 1000 subjects in group 2 (control group) receive a placebo. For the drug group, the mean score on the ESP test was 15, SD=4. For the no-drug group, the mean =9, SD=9. Does taking this drug increase test scores? Test your hypothesis at 5% significance level. (Include null and alternative hypothesis, test statistic, p-value, and conclusion)  

Answer 1

We want to test that taking this drug increase test scores

u1:- population mean test score of after taking the drug

u2:- Population mean score test score of not taking the drug

The null & alternative hypothesis

Ho:- u1-u2 = 0 vs Ha:- u1 - u2 > 0

Group 1: treatment group: who takes drug before the test

Group 2: control group: who takes doesn't take the drug before the test

P- value :

P-value = P(tn1+n2-2 > t )

= P(t900+1000-2 > 18.429)

= P(t1898 > t )

=0

The decision:-  Reject Ho if P-value < alpha

Alpha = 0.05

P-value= 0 < alpha = 0.05

So we reject Ho

Conclusion:- We may conclude that the data provides sufficient evidence to support the claim that the drug increases test scores.

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Test Statistics t-statistic is computed as follows: X - X2 In, -1);{ +(12-1)3 (1+1) 71-19-2 15-9 = = 18.429 (900-142+(1000-191 (900 + 1000) 1 ) 900-1000-2