test statistic and probaility
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
(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
(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.
We decline to reject at significance level α=0.05
i think i have problem in (a), and (c) please let me know how to solve this problem