Assume that

X1, . . . ,X10 ∼ Normal(μ1, σ1^2) and that Y1, . . . , Y20 ∼ Normal(μ2, σ2^2).

None of the population parameters are known. Let = μ1 − μ2.

To test H0 : ≥ 0 versus H1 : < 0 at significance level α = 0.05, we observe samples ~x and ~y.

(a) What test should be used in this situation?

If we observe ~x and ~y that result in¯x = −0.82, s1 = 4.09, ¯y = 1.39, and s2 = 1.22, then what is the value of the test

statistic?

(b) If we observe ~x and ~y that result in s1 = 4.09, s2 = 1.22,, and a test statistic

value of 1.76, then which of the following R expressions best approximates the

significance probability?

i. 2*pnorm(-1.76)

ii. pt(-1.76,df=28)

iii. pt(1.76,df=10)

iv. pt(-1.76,df=10)

v. 2*pt(1.76,df=28)

(c) True of False: if we observe ~x and ~y that result in a significance probability of p = 0.96, then we should reject the null hypothesis.

i try to solve this problem ......by using R program

(a)We should use Welch’s approximate T-test in this situation.

> v=(((((4.09)^2)/10)+(((1.22)^2)/20))^2)/((((4.09/10)^2)/9)+(((1.22/20)^2)/19))

> v

[1] 162.5339

> qt=qt(.975,v)

> qt

[1] 1.974667

> tw=((-.82-1.39)-0)/(sqrt(((4.09^2)/10)+((1.22^2)/20)))

> tw

[1] -1.671927

ᅵtwᅵ=1.671926<qt=1.974667

We decline to reject at significance level α=0.05

(b)

(ii) pt(-1.76,df=28)

(c)

i think i have problem in (a), and (c) please let me know how to solve this problem