Random sampling from two normal populations produced the following results:

x₁ = 412S₁ = 128n₁ = 150

x₂ =405S₂ = 54 n₂ = 150

a)Can we infer at the 5% significance level that 1 is greater than 2?

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 x₁ = 409.

g)Discuss the effect of decreasing x₁.