Statistics 1 revision quiz

Apr9

Written by Colin + in quizzes, statistics 1.

Statistics 1 quiz

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This quiz is based on the EdExcel S1 syllabus - the other exam boards are substantially different, so this may not be for you. It's designed to get you working on the basics of S1 - the stuff you'll need to have down pat if you want to do well.

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Question 1

You know $S_{xx} = 20$, $S_{yy} = 60$ and $S_{xy} = 48$. Also, $\bar{x} = 4$ and $\bar{y} = 10$. What is the regression line of $y$ on $x$?

A	$y-10 = 3(x-4)$
B	$y - 10 = 2.4(x-4)$
C	$y + 10 = 2.4(x+4)$
D	$y-10 = 0.8(x-4)$
E	$y+10=0.8(x+4)$

Question 2

Time	Frequency
0-10	7
10-20	15
20-40	3

Use linear interpolation to estimate the median of this data. Give your answer to three significant figures.

A	20.0
B	13.5
C	15.0
D	12.5
E	13.7

Question 3

What is ${\rm Var}(5X + 3)$?

A	$25{\rm Var}(X)$
B	$25{\rm Var}(X)+3$
C	$25{\rm Var}(X)+9$
D	$5{\rm Var}(X)+3$
E	$5{\rm Var}(X)$

Question 4

What does a product moment correlation of 0.4 mean?

A	The dependent variable causes the effect in the independent variable. Hint: Read that back and see if it makes any sense.
B	There is a strong positive correlation between the variables.
C	The variables are uncorrelated.
D	There is a moderate positive correlation between the variables.
E	The independent variable causes the effect in the dependent variable. Hint: Nope. Stork population is strongly correlated with births - but they don't cause them.

Question 5

Time	Frequency
0-10	7
10-20	15
20-40	3

Estimate the mean of these data. Give your answer to three significant figures.

A	117
B	15.0
C	8.33
D	14.0
E	14.7

Question 5 Explanation:

$\frac{5\times7 + 15\times 15 + 30\times 3){25} =14.$

Question 6

If you know $\mu$, $sigma$ and $x$, what is the formula for the $z$-score?

A	$z = \frac{x-\sigma}{\mu}$ Hint: That's not it!
B	$z = \mu + \sigma x$ Hint: Nope, sorry!
C	$z = \sigma + \mu x$ Hint: Nut-uh.
D	You look it up in the table! Hint: No! That's how you get between $p$ and $z$.
E	$z = \frac{x-\mu}{\sigma}$ Hint: Correct!

Question 7

How can you tell if two variables are independent?

A	$P(A \| B) = P(A)$
B	$P(A \cap B) = P(A) \times P(B)$
C	$P(A \cup B) = P(A) + P(B)$ Hint: No, that's mutually exclusive.
D	The probability of them both happening is 0. Hint: No, that's mutually exclusive.
E	$P(A \cup B) = P(A) \times P(B)$

Question 8

A discrete random variable has the probability function $p(X=x) = \frac{k}{x}, ~ x=1,2,3,4,5,6$. What is $k$?

A	$\frac{137}{60}$
B	$21$ Hint: No.
C	$\frac{49}{20}$ Hint: No, that's the sum of the probabilities!
D	$\frac{20}{49}$ Hint: Yep!
E	$\frac{60}{137}$

Question 9

What is $E(10X + 5)$?

A	$10E(X)$
B	$10E(X)+25$
C	$100E(X)+5$
D	$100E(X)$
E	$10E(X)+5$

Question 10

Of 100 cyclists, ten are doped to the eyeballs on performance-enhancing drugs. The test for drugs is 90% accurate - if you fail the test, there's a 90% chance you're cheating; if you pass, there's a 90% chance you're clean. A cyclist fails the drugs test. What is the probability she is a drugs cheat?

A	90% Hint: No! Booby trap :o)
B	50% Hint: Yes!
C	81% Hint: No.
D	19% Hint: No.
E	10% Hint: No.

Question 10 Explanation:

The test will catch 9 of the ten cheats, but also implicate 9 of the 90 clean riders - so 9 out of the 18 who fail the test are cheats, but the other 9 are false positives. $P( drugs | fail ) = $\frac{P(drugs and fail) }{P(fail)} = \frac{0.1 \times 0.9}{0.18} = 0.5$

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Colin

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.

Statistics 1 quiz

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