Solutions XP83 2012 Final

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Question 1

(1)  mean is 1, stan dev is 1
(2) mean is 2, stan dev is 1
(3) mean is 1, stan dev is 2
(4) 1
(5)  1 +/- 2
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Question 2

(1)
 .6*.002 + .4*.01346 = 0.006584
(2)
.4*.0333 = 0.01332
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Question 3

(1) .25
(2) .75
(3) 2
(4) .5
(5) .7071

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Question 4

(1) .24
(2) .6
(3) .6
(4) yes
(5) yes
(6) .4
(7) .24
(8) yes
(9) 0

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Question 5

(1) .007
(2) .4*.2 + .6*.1 = 0.14
(3) (.4^2)*.01 + (.6^2)*.01 + 2*.4*.6*.007 = 0.00856

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Question 6

(1) .1
(2) .01
(3) .1
(4) .84
(5) 1000
(6) 1000
(7) 0
(8) 2*var(B) = 2*1000^2 = 2*1,000,000 = 2,000,000.
(9) +\- 2*sqrt(2)*1000 = +/- 2828.

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Question 7

(1)  .095
(2) 
> se = sqrt(.095*(1-.095)/1000)
> se
[1] 0.00927227
> ci = .095 + 2*.00927*c(-1,1)
> ci
[1] 0.07646 0.11354

(3) 
> phat = 95/1000
> z = (phat-.15)/sqrt(.15*(1-.15)/1000)
> z
[1] -4.870882
reject.
(4) 
yes, it is a clear reject.

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Question 8

(1) 
I did not tell you if they took the course but it does not make
much difference.

Without course:
18.47174 + 95*0.81866 +2*7.311*c(-1,1)
[1]  81.62244 110.86644
With course subtract .85
18.47174 + 95*0.81866 +2*7.311*c(-1,1)-.84577
[1]  80.77667 110.02067

(2)
.81866 +2*.07*c(-1,1)
[1] 0.67866 0.95866

(3) 

t is 11.79, p-value is 0, reject

(4)

-.84577 + 2*1.478*c(-1,1)
[1] -3.80177  2.11023

(5)
fail to reject.

(6)

No. The sign is negative but the magnitude is insignificant both
in that you cannot reject 0 and the confidence interval only includes
values of little practical importance.

(7)

> t= (.81866-1)/.06943
> t
[1] -2.611839

reject.


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Question 9

(1) d
(2) c
(3) a
(4) b
(5) d
(6) b
(7) a
(8) d

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Question 10

(1) T
(2) F
(3) T
(4) F
(5) F
(6) F
(7) T
(8) T
(9) F
(10) T
(11) T
(12) T
(13) T
(14) T
(15) T
(16) T
(17) T
(18) F
(19) F
(20) F

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Question 11

with p1=.1 we have 
         R     
      0    1
 0  .25  .25

Q

 1  .45   .05

(1) 

p(Q=1,R=1)=
p(Q=1)p(R=1 | Q=1) = .5*.1 = .05.

(2)

p(R=1)=
p(Q=0,R=1)+p(Q=1,R=1) = .5*.5+.5*.1 = .3.

(3)
p(Q=1|R=1) = p(Q=1,R=1)/p(R=1) = .05/.3 = .167.

(4)
p(Q=1 | R=0)=p(Q=1,R=0)/p(R=0) = .45/.7 = .643.

(5)

If he says yes, the investigator would guess he
answered the digit question.
If he said no, it is still not too different from 50-50
on the question.

So, the respondent does seem pretty safe answering yes
to the drug question of that is the truth.

(6)

p = p(Q=0,R=1) + p(Q=1,R=1) = .25 + .5p1.

Also useful to note that
p1 = 2p-.5.

(7)

450/1000 = .45

(8)

2*.45-.5
= 0.4

(9)

yes, the estimator for p1 is a linear function
of the estimator for p.

(10)

se = sqrt(phat*(1-phat)/1000)
> se
[1] 0.01573213

phat + 2*se*c(-1,1)
[1] 0.4185357 0.4814643

(11)

> cip
[1] 0.4185357 0.4814643
> 2*cip-.5
[1] 0.3370715 0.4629285

(12)

> p1hat = 200/500
> p1hat
[1] 0.4
> se1 = sqrt(p1hat*(1-p1hat)/500)
> cip1 = p1hat + 2*se1*c(-1,1)
> cip1
[1] 0.3561822 0.4438178

(13)

The one where you know the questions
(0.3561822 0.4438178) is smaller.

It makes sense that with more information
your ci should be smaller!

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Question 12

12.1     20

12.2     59

12.3     25

12.4     34

12.5     22

12.6     25