Describe what happens when the sample standard deviations

Question

Random sampling from two normal populations produced the following results:

x 1 = 412           s1 = 128       n1 = 150

x2 = 405           s2 = 54          n2 = 150

a) Can we infer at the 5% significance level that μ₁ is greater than μ₂?

b) Repeat Part a decreasing the standard deviations to s1 = 31 and s2 = 16.

c) Describe what happens when the sample standard deviations get smaller.

d) Repeat Part a with samples of size 20

e) Discuss the effects of decreasing the sample size

f) Repeat Part a changing the mean of sample 1 to x' = 409

g) Discuss the effect of decreasing   x'₁ = 1.