Assignment X1,X2,X3,X4, few general questions.

[joshinupur2000]

Hi John,
could you explain to me the exact procedure for drawing a box plot. it's not clear to me.
for example in assignment X1-Q-X1.8.

In assignment X2-Q-X2.14-(iii)- how did they get the last step- sample mean follows chi-square with 20df?
In assignment X3-Q-X3.8-(iii)- i didn't understand the equations they've written to get the accurate confidence interval.
In assignment X4-Q-X4.9-(i)- what is alpha? why do we look under 0.05% in the chi-square tables?
and in the solution of (ii), how do get the numbers 910.5,992.0,89.5,8.010?
how do you get the observed frequencies 904,998,91,7?
in a t-test we know that if t-calculated>t-tabulated then we reject H0.
and if t-calculated<t-tabulated then we accept H0.
can we write this when we draw our conclusion? I'm asking because i haven't seen this been used.

 

[John Lee]

could you explain to me the exact procedure for drawing a box plot. it's not clear to me.
for example in assignment X1-Q-X1.8.

Boxplots are on page 21 of chapter 1. The box goes from the lower quartile to the upper quartile - with a line in it to denote the median. The "whiskers" go from the boxes to the highest and lowest values.

In assignment X2-Q-X2.14-(iii)- how did they get the last step- sample mean follows chi-square with 20df?

Since we're told in the question that it's a gamma(2,0.1) we have alpha = 2 !

In assignment X3-Q-X3.8-(iii)- i didn't understand the equations they've written to get the accurate confidence interval.

Using the formulae from page 18 of Chapter 11 Section 4.2

A 99% confidence interval has 0.5% either side.

Hence we have:

P(X>= 10) = 0.005

and

P(X<=10) = 0.005

In assignment X4-Q-X4.9-(i)- what is alpha? why do we look under 0.05% in the chi-square tables?

I'm a bit confused there is no alpha is this question.

For 1-sided tests we look at the 5% value to see if it's significant. Our value exceeds this so it is significant. We are simply showing that it exceeds even higher tail values and so is very significant.

and in the solution of (ii), how do get the numbers 910.5,992.0,89.5,8.010?

We have simply put in the given value of q from the question into the formulae!

how do you get the observed frequencies 904,998,91,7?

They are given in the question!

in a t-test we know that if t-calculated>t-tabulated then we reject H0.
and if t-calculated<t-tabulated then we accept H0.
can we write this when we draw our conclusion? I'm asking because i haven't seen this been used.

It depends what the H1 is. If it is a greater than then you are correct. If it is a less than then it's the other way round.

Yes you can write this in the conclusion .

See Eg 12.1 Method 2