Mango –
The test is to determine whether or no USED measures are significantly
different for Nox from the NEW cars. The assumptions here are that
both measures come from randomly distributed, independent populations
that can be against the bell curve called a "Student t-distribution".
Charts for Student T's are in back of every statistics book.
You'll be looking to see if you can validate this hypothesis:
H2: the USED results are within a 95% confidence level of new car
measures
Looking at a T-distribution chart for (N1 + N2 – 2) degrees of
freedom, we're looking for 45 degrees of freedom and a T < 2 at the
95% level. (We'll tighten this test up later).
Working with two means from normal distributions, especially with this
small sample size, requires you to figure you’re a pooled variance.
Of course, VAR = SD(SQUARED)
SD1 = 3.33 VAR1 = 10.9
SD2 = 4.66 VAR2 = 21.2
VAR = VAR1/N1 + VAR2/N2 = 1.33
Now your t value is T = (M2 – M1)/SQUARE ROOT(VAR) = (56.8 –
53.3)/1.15 = 3.04
This value is outside the 95% confidence interval, as T > 2.0
If you want a 99% confidence interval, ask in your hypothesis – is T >
2.7?
It is, making the hypothesis that USED means are different from those
for NEW vehicles.
Best regards,
Omnivorous-GA |
Clarification of Answer by
omnivorous-ga
on
10 Nov 2002 11:59 PST
Mango --
The GA editor isn't being faithful to my Word document, in which I
created the original. Please note that these formulas should read:
(N1 + N2 - 2) degrees of freedom
(M2 - M1)/SQUARE ROOT(VAR)
In other words, those blocks should be minus signs (-).
If this is still unclear, please let me know before rating this
question.
Best regards,
Omnivorous-GA
|
Request for Answer Clarification by
mango1952-ga
on
10 Nov 2002 21:53 PST
CAN YOU PLEASE SIMPLFY THE ANSWERS TO THE QUESTIONS, AS THESE ARE
RESEARCH METHODS SUBJECTS (STATISTICS). PLEASE WORK OUT THE FORMULA SO
THAT IT WILL BE UNDERSTOOD BY THE UNIVERSITY LECTURER. STICK TO THE
QUESTIONS?
MANY THANKS
MANGO
|
Clarification of Answer by
omnivorous-ga
on
11 Nov 2002 06:21 PST
Mango --
If you can clarify what your instructor wishes to see, it might help
focus this answer. This is precisely how I'd state the hypothesis to
them:
The test is to determine whether or no USED measures are significantly
different for Nox from the NEW cars.
Our first hypothesis will be:
H1: the USED results are within a 95% confidence level of NEW car
measures
We'll also test the same means for the USED vehicles with a tighter
99% confidence level in a second hypothesis:
H2: the USED results are within a 99% confidence level of NEW car
measures
The assumptions here are that both measures come from randomly
distributed, independent populations that can be against the bell
curve called a "Student t-distribution".
Looking at a T-distribution chart for (N1 + N2 – 2) degrees of
freedom, we're looking for 45 degrees of freedom and a T < 2 at the
95% level; T < 2.7 for the 99% confidence level.
Working with two means from normal distributions, especially with this
small sample size, requires you to figure you’re a pooled variance.
Of course, VAR1 = SD1(SQUARED). All of your statistics are:
N1 = 19 N2 = 28
M1 = 53.3ppm M2 = 56.8ppm
SD1 = 3.33 VAR1 = 10.9
SD2 = 4.66 VAR2 = 21.2
The pooled variance for a small sample size like this is:
VAR = VAR1/N1 + VAR2/N2 = 1.33
Now your t value is T = (M2 – M1)/SQUARE ROOT(VAR) = (56.8 –
53.3)/1.15 = 3.04
H1: This value is outside the 95% confidence interval, as T > 2.0
The hypothesis fails.
H2: It is also outside the 99% confidence level, as T > 2.7
The hypothesis fails.
Thus, we conclude that pollution controls for Nox are deteriorating in
USED vehicles over the 8+ month period.
Best regards,
Omnivorous-GA
|
Clarification of Answer by
omnivorous-ga
on
11 Nov 2002 06:22 PST
Again, the blocks in the latest clarifications should be minus (-) signs.
Best regards,
Omnivorous-GA
|
