"Malaysia Prime Minister Mahathir Mohamad and the Sultan of Johor are seen in a blue Proton Saga... "When asked whether there is any tension with the sultan, Dr Mahathir said: “No, I don’t see anything because I went to see him and he drove me to the airport. I don’t want to comment on the sultans because if I say anything that is not good then it’s not nice because he is the sultan”"

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Friday, May 06, 2005

"It is dangerous to be right when the government is wrong." - Voltaire

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My statistics textbook reads like an advertisement for Minitab and PHStat (some statistical programs).


More sample exam questions:

1. A professor is attempting to predict the marks that students get for his final exam by regressing them against the amount of time spent studying for it. He has observations on these 2 variables for 6 students, as shown below:


Time spent studying (hours) Marks
103 58
90 65
100 60
80 70
76 72
70 80


a) Obtain the least square estimates of the intercept and slope coefficient in the professor's linear regression of Marks on Time spent studying.

(Punching my calculator, I get b0 = 119.555 and b1 = - 0.608)

b) Interpret the estimated slope coefficient and test whether it is different from zero at the 5% significance level.

(For every additional hour spent studying, the students lower their marks by 0.608 points. I don't feel like doing the hypothesis testing, so I'll skip it. Anyhow it's hard to present online.)

c) How many hours should one study to get 100 marks?

(yi = b0 + b1xi
100 = 119.555 - 0.608xi
xi = 32.16

One should study for 32.16 hours to get 100 marks.
)

d) Can the estimated intercept value be sensibly interpreted? What lessons can we learn from this regression analysis?

(No. You can never get more than 100 marks. Don't study too much, for after some time you'll get negative returns like these poor chaps above.)


2. The average NUS student can pick 5 modules to study per semester. He has a choice of Type A modules (Mean grade 4.5, variance 0.5) or Type B modules (Mean grade 5.0, variance 1). The modules are assumed to be independent (ie covariance 0), and due to the bell curve grading system, the marks for the modules are normally distributed.

a) If he takes 3 Type A and 2 Type B modules, what is his mean CAP for the semester?

((3 x 4.5 + 2 x 5.0)/5 = 4.7)

b) What is the probability that his semestral CAP drops below 4.0 if he takes 5 Type A modules?

(P(X<20) = P(Z<20-22.5/25) = P(Z<-1) = P(Z>1) = 0.1587)

***

"Punctuated equlibria and genetic drift are already explained in the various posts. With regard to the former, nobody quite understands what Gould and Eldridge was rambling about and it certainly changed over time. So, forget about it."

Heh.

***

Pages which play songs after loading are really annoying. I was happily listening to my Mass In B Minor, Bwv 232 - Symbolum Nicenum (Credo) - I. Credo In Unum Deum, when the strains of a guitar and a guy singing became audible (Collide - Howie Day, I later found out). Everytime this happens I get this irrational fear that somehow my MP3 has become corrupted

And when one loads more than one of them at a time, thanks to the joys of tabbed browsing, a big mess is created. Luckily I have the 'Zap Plugins' bookmarklet.

***

This page on Tym's blog has become the (semi-)official bulletin board for 2A03A 2001 / 1A03A 2000. Ah, the wonders of modern communication.

***

The NUS network doesn't block access to Chick.com, unlike SCV (yes, it's still blocked by SafeSurf). This, of course, must be because there are too many fundies on campus.


I was very offended by this leaflet I found in the Arts Canteen. The cover was decorated with bright colours, and had ambiguously worded lines promising hope and that sort of thing. Of course, this got my guard up.

Sure enough, when I looked inside the leaflet promoted "the healing power of Jesus", and was complete with fulsome testimonials.

If health product makers can be jailed for false advertising, or at the very least have to put up disclaimers saying that their products' efficacy has not scientifically proven, what more this religious snake oil? Especially since many of the diseases cures are promised for are terminal ones, making this a crime a few order of magnitudes worse than selling magic stones or normal snake oil (which don't promise to save your soul or your life, and at least are tangible and can be held in your hands).
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