ECMT1010 - Revision Questions (1 Viewer)

[stazi]

Just going through past quiz possible questions, any one know what the 'modal class' of a histogram is?

the heaviest populated class. Think 'mode' in statistics.

 

[ressul]

Q48 is in the attachment..

Why do u make S *1.01?

 

[stazi]

Anyone knows how to do Q11, I); Q21,h); Q48 and the full process for Q57c)?

q11 has been done for you
q21 h is a misprint. I'm assuming it means g) not c)

 

[stazi]

can i ask, how to calculate marginal distribution and coniditional distribution?thanks~!!!!!!!!

This wasn't explained that clearly.

Let's suppose
X
0 .25
1 .35
2 .40

The marginal distribution of X looks like:
P(X=0) = .25
P(X=1) = .35
P(X=2) = .40

Conditional probability is obtained using this formula:
P(A|B)=P(A&B)/P(B)

 

[yvonne_710]

This wasn't explained that clearly.

Let's suppose
X
0 .25
1 .35
2 .40

The marginal distribution of X looks like:
P(X=0) = .25
P(X=1) = .35
P(X=2) = .40

Conditional probability is obtained using this formula:
P(A|B)=P(A&B)/P(B)

i almost understand what is marginal distribution, but for conditional distribution.....

 

[yvonne_710]

Why do u make S *1.01?

bcz u need to pay extra one month, without 1.01, there are only 35 months, u need pay the 36th month ..

 

[stazi]

i almost understand what is marginal distribution, but for conditional distribution.....

condition distribution just uses the condition probability formula.

So it'd be
P(X=1|Y=1)=
P(X=2|Y=1)=
P(X=3|Y=1)=
etc.

 

[Rorix]

i almost understand what is marginal distribution, but for conditional distribution.....

your total possibilities has been reduced because you limit it to the cases where Y=1 - or whatever the condition happens to be. e.g. if P(Y=1)=.4 and P(Y=0)=.6 [marginal distribution] then your new probabilities will all be /.4, so P(X=1 and Y=1)=.2 will be .5 in the condition distribution

As P(A|B) = P(A and B)/P(B) as stas said

 

[sarevok]

Hmm...for these test the slope questions, don't we have to make some sort of assumption? Like something about iid? I think Tig said something about this in consultation but notes aren't really clear.

 

[yvonne_710]

oh,well...thanks guys~~~~~~~~~~~

 

[ressul]

Question

See Q33 C):
y(hat)=41.6667-2/3X
H0: B1=0; H1: B1<0
In the answer, its conclusion is Don't Rej H0
Does it mean that the slop coefficient is NOT negative?
But in the equation, the slop IS negative, which is -2/3.
Is my thinking right? How should we explain this?

 

[stazi]

did we ever get to the bottom of using a p-value hypothesis test on a t-stat?
I understand Z stat but tstat escapes me.

 

[jpr333]

It's not a probelm cause of the assumptions you use for p values, something like P(s) > 5 and P(1-s) > 5 or whetever it is assume normality and the t distribution is obselete. This raises another question, when actually using T distribution do you assume normality or what? What do you actually state to justfy using T stats cause if you assume normality why not just use the z tables. And another thing for hypothesis testing when can you use the normal tables, I have heard something like when n>100 use z tables but the CLT is for n>30, and if you can't use the z tables ie n<30 what do you say in your assumptions again for justifying the use of a t stat, n<30 therefore assume t'ially distributed. If anyone can clarify I would be grateful.

Ps I don't believe in paragraphs.

 

[monkey187]

hey i was wondering how to do the confidence questions where they give you the sum of the stastics. like q13, 18 etc...

how can u find the confidence interval without the variance!!

 

[jpr333]

Without the variance you use the t critical values! (I think) Wait that might be population variation vs sample variance. You may have to calculate it yourself if possible or it's a proportion qs perhaps.

 

[yvonne_710]

See Q33 C):
y(hat)=41.6667-2/3X
H0: B1=0; H1: B1<0
In the answer, its conclusion is Don't Rej H0
Does it mean that the slop coefficient is NOT negative?
But in the equation, the slop IS negative, which is -2/3.
Is my thinking right? How should we explain this?

its nearly same like q2(e).............

 

[stazi]

It's not a probelm cause of the assumptions you use for p values, something like P(s) > 5 and P(1-s) > 5 or whetever it is assume normality and the t distribution is obselete. This raises another question, when actually using T distribution do you assume normality or what? What do you actually state to justfy using T stats cause if you assume normality why not just use the z tables. And another thing for hypothesis testing when can you use the normal tables, I have heard something like when n>100 use z tables but the CLT is for n>30, and if you can't use the z tables ie n<30 what do you say in your assumptions again for justifying the use of a t stat, n<30 therefore assume t'ially distributed. If anyone can clarify I would be grateful.

Ps I don't believe in paragraphs.

n<30: Assume normal distribution. Can use t statt
30<n<130: Use CLT. Say that t is a robust estimator
n>130: Use Z table. Use CLT.

 

[stazi]

hey i was wondering how to do the confidence questions where they give you the sum of the stastics. like q13, 18 etc...

how can u find the confidence interval without the variance!!

q13:
You're given the sum of X: 56. So the mean = 56/n =56/10
You're given the sum of X^2: 360

To find the variance remember the formula:
E(X^2)-[E(X)]^2

So it'd be 360-5.6^2

And don't forget to square root it. We don't need the variance. We need the standard deviation.

 

[sarevok]

From my notes,

Given that population is normal, and when o is uknown, use t-stat.
n<15 do not use t-stat unless given that population is normal.
15<n<40 use t-stat unless strong skewness in population.
n>40 use t-stat even if there is strong skewness.
n>120 t distribution approximates normal distribution, use z tables.

 

[stazi]

From my notes,

Given that population is normal, and when o is uknown, use t-stat.
n<15 do not use t-stat unless given that population is normal.
15<n<40 use t-stat unless strong skewness in population.
n>40 use t-stat even if there is strong skewness.
n>120 t distribution approximates normal distribution, use z tables.

What i posted is what an exam marker told my tutor before our last tutorial.
The text book also says this.