General
What struck me particularly this year was the enormous number of students making elementary errors {
• for example, over 20 candidates told me that the sample variance is equal to P x2 i −nx¯2
or to 1
n P x2
...
General
What struck me particularly this year was the enormous number of students making elementary errors {
• for example, over 20 candidates told me that the sample variance is equal to P x2 i −nx¯2
or to 1
n P x2 i − x¯2 or to n−1 1 (P x2 i − nx¯) . Not only is the correct formula easy to
remember, but it is also provided on the formulae sheet, so there is no excuse for
getting it wrong. Looking at the scripts, some of you seem to be mixing up the sample
variance, Sx2, with the deviation sum of squares, Sxx, which is only used in the chapter
on linear regression.
• Another error which has cropped up this year, but which I have hardly ever experienced
before, is the inability to tell the difference between sample mean and expectation, or
between sample variance and variance. If you write µ = n1 P xi or Var (Y ) = s2 Y ,
you will lose marks every time. A very large number of scripts exhibited an error of
this kind. The most important lesson you need to take away from this module is that
parameters (µ, σ2, θ, α, β) are unknown theoretical quantities and sample statistics (¯ x,
s2, θ^, a, b) are quantities calculated from the data: they are completely different, and
must not be confused with each other.
• A lot of you forgot to use the binomial coefficients when calculating binomial probabilities, so you just had P(X = x) = θx(1 − θ)k−x. You can detect this error by checking
that your probabilities sum to 1, or by looking at the formulae sheet.
If you are going to convert a probability expressed as a fraction into a decimal, you should be
using four decimal places, not two: 2dp is simply not enough for a probability. On the other
hand, please don’t imagine that I want you to work in fractions at all costs: I am not happy
to see you report a probability as 2;10 473 ;904 ;875 and I would much rather see this as a decimal.
Another general point: if you are working out a sample mean, you don’t have to write
x¯ = 1
10(6 + 3 + 2 + 4 + 19 + : : :) { I am willing to assume that you are using the right formula
if you get the right answer.
Quite a few marks were lost when reporting the results of hypothesis tests. If you can’t reject
H0 it is wrong to say \there is significant evidence in support of the null hypothesis." If you
can reject H0 at the 5% level but not at the 1% level, it is completely wrong to say \We accept
H0 because there is highly significant evidence in favour of it." : you must not try to hide
the fact that you have uncovered significant evidence against the null.
While on the subject of hypothesis tests, don’t forget to interpret your conclusion: don’t say
\Reject H0", but instead say \Reject H0: there is significant evidence that the samples come
from populations with different variances.
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