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.

-----------

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>

a) Compute the grand mean and respective variances for A, B, C, or D. [ 5 marks ]

b) Complete the ONE-WAY ANOVA table, where "Treatment" refers to the four different brands of antacid. [ 9 marks ]

c) Test and conclude at 5% significance level whether there is sufficient evidence to claim that the four different brands are having the same average speed in relieving gastric problems.

My answers are:

a)
Grand mean: 27.9
Variance A: 12.67
Variance B: 82
Variance C: 8.25
Variance D: 16.67

b)
Df(Tr) = 3
Df(E) = 12
Total = 15

SS(Tr) = 288.21
SS(E) = 358.77
Total = 646.98

MS(Tr) = 96.07
MS(E) = 54.9

F = 1.75

c) Null Hypothesis: All means are equal.
Alt. Hypothesis: Not as stsed in H(null).

F alpha/2, k-1, N-k = F 0.05, 3, 12
= 3.49

Conclusion:

Since F=1.75 < Fcritical =3.49, we fail to reject Ho at 5% sig level.

There is sufficient evidence to prove that H1 is true at 5% sig level.

ie. The claim that the four different brands are having the same average speed in relieving gastric problems is not true.

I think I'll post another question tmr. For those who know how to do this question, PLEASE TAG to tell me your answers. Or else I'm gonna fail MathStats.

Your participation is greatly appreciated (:

Crys.

My dearest cousins!!!

This was taken for the 'fieldtrip' to PastaFresca.

Jolene looks really pretty that day!

Thus, I took a picture with her!!!

These are actually test tubes from my Basic Microbiology Lab Session!
We had to do all that agar testing, TSI... and others.

I guess Microbes are kinda useful for colours? Hehe!

That guy in the suit there isn't my lecturer.

In fact, he's my classmate!

It's so rare to see him in such formal clothes!!
The whole get up is for the Communication Skills Presentation we had that day! =D

And yes, for the ex SPS people, That's Andy. That white guys you people tend to call him. He looks kinda tanned now, huh? :)

The groups there were supposed to present that day!

My group!

We did 'Save the Earth'. =D It was our topic! (:

And I had Dinner with Darling Daphne at Sakura on Tuesday!
It was her treat, and it was really ex! :(

But it's buffet, and I paid $9!
The sad part is that $9 isn't even half of my bills!

But Thanks Daphne!! Lovies my dear! =DD

Ah ma signs off here. ;)