Question

> x=c(5,3,1,6,4,3,2,6,7)

> y=c(7,4,1,8,5,2,4,7,9)

> mean(x)

[1] 4.111111

> mean(y)

[1] 5.222222

> cor(x,y) # + indicates consistency, more power

[1] 0.943973

> t.test (x,y,paired=T) #sig because of + correlation

   Paired t-test

data: x and y

t = -3.1623, df = 8, p-value = 0.01335

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

-1.9213584 -0.3008638

sample estimates:

mean of the differences

             -1.111111

>

What conclusions can be made regarding statistical significance?

Would that conclusion change with a 1-tailed test? Why or why not?

Answer 1

Conclusion:

     The t value of the test is -3.1623 with a p-value < 0.05. So there is suffcient evidence at 5% level of significance to reject the null hypothesis and it can be concluded that there is significant difference in the population means betweeen the dependent populations x and y. The conclusion would not change with a 1-tailed test, because the p-value for the 1-tailed test will be lesser than the p-value of the 2-tailed test by 50%. So the reduction in p-value further would not change the decision of rejection in this case.