a) Test and conclude the hypothesis of equal variances at 5% significance level. Assume that both samples are independent and drawn from normal populations.
[ 12marks ]

b) Test and conclude whether the battery type A has a longer life-span than that of battery type B at the same significance level in part (a).
[ 8 marks ]

My answer:

a)
Ho: varianceA = varianceB
H1: varianceA doesn't = varianceB

Normal population -> use Z test

alpha = 0.05
alpha/2 = 0.025
Zalpha/2 = 1.96

Var(A) = 650.25
Var(B) = 1075.84

Z = [(x1 - x2)-(U1 - U2)]/Root of [(VarB/n1) + (VarA/n2)]
= 0.706
= 0.71

Since Zalpha/2 = 1.96 > Z = 0.71, we fail to reject Ho at 5% sig level.

There's insufficient evidence to prove that H1 is true at 5% sig level.

That's all. I think I did this one wrongly though.

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I was watching Mulan just now, and it reminded me of how much I love this song. There's 2 versions of it. The one sung by Christina Aguilera, and this one.


Look at me
I will never pass for a perfect bride,
or a perfect daughter
Can it be
I'm not meant to play this part?

Now I see
that if I were truly to be myself
I would break my family's heart

Who is that girl I see
Staring straight back at me?
Why is my reflection someone I don't know?
Somehow I cannot hide
Who I am, though I've tried
When will my reflection show
who I am inside

When will my reflection show
who I am inside

Crys rmb her <3>