Question

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

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

> mean(x)

[1] 3.888889

> mean(y)

[1] 5.222222

> sd(x)

[1] 1.900292

> sd(y)

[1] 2.728451

> t.test(x,y,var.equal=T)

   Two Sample t-test

data: x and y

t = -1.203, df = 16, p-value = 0.2465

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

95 percent confidence interval:

-3.682888 1.016221

sample estimates:

mean of x mean of y

3.888889 5.222222

> t.test(x,y,var.equal=F)

   Welch Two Sample t-test

data: x and y

t = -1.203, df = 14.283, p-value = 0.2485

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

95 percent confidence interval:

-3.706056 1.039389

sample estimates:

mean of x mean of y

3.888889 5.222222

>

What conclusion can be made regarding the first t-test in terms of statistical significance?

Does inequality of variance change that conclusion?

Modify the code for the first t-test to test the alternative hypothesis that ux<uy

Answer 1

What conclusion can be made regarding the first t-test in terms of statistical significance?

since p-value = 0.2465 > 0.05

we fail to reject the null hypothesis , , we conclude that there is not sufficient evidence that there is difference between x and y.

Does inequality of variance change that conclusion?

No, because still p-value = 0.2485 > 0.05

Modify the code for the first t-test to test the alternative hypothesis that ux<uy

t.test(x,y ,alternative="less", var.equal=TRUE)