Statistical Inference

[deelaw007]

It's a rule that when we find z value at a certain point like at 2500 in part a, the answer we are getting is for values that lie under 2500, i.e. less than 2500. If we have all those less than that value, and the total is always 1, what do we get when we subtract from the total 1? probably the ones which are not less than X, and not less than X means greater than X. Got it?

nope

 

[Eugene99]

nope

why not?
Leave the logic for a while, you just have to remember that if question asks for 'greater than' find in the normal way, then subtract from 1 at the end, that will get you the 'greater than'

 

[deelaw007]

why not?
Leave the logic for a while, you just have to remember that if question asks for 'greater than' find in the normal way, then subtract from 1 at the end, that will get you the 'greater than'

if it says less than?

 

[Eugene99]

if it says less than?

no the question is 'more than' but before subtracting, our answer is for at that point or less than that, you could say it says AT LEAST 2500, which covers 2500 and everything less than that. Since 1 is total, subtracting from 1 will mean we get all which is not 'less than' and not less than is of course greater than.

 

[deelaw007]

no the question is 'more than' but before subtracting, our answer is for at that point or less than that, you could say it says AT LEAST 2500, which covers 2500 and everything less than that. Since 1 is total, subtracting from 1 will mean we get all which is not 'less than' and not less than is of course greater than.

 

[Eugene99]

if it says less than?

oh you asked IF it says less than? sorry I misread
if it says less than, then we don't subtract the answer is the final answer
get that?

 

[deelaw007]

oh you asked IF it says less than? sorry I misread
if it says less than, then we don't subtract the answer is the final answer
get that?

yes

 

[Eugene99]

see this:

when it's Z>1.342
that symbol before 1.342 means the corresponding value of z from the table

 

[Eugene99]

I hope that's it?

 

[deelaw007]

there are fe

I hope that's it?

there r few more questions that i'll post

 

[Eugene99]

there are fe

there r few more questions that i'll post

did you try yourself?

 

[deelaw007]

did you try yourself?

wo sampling distriution

 

[Eugene99]

you can post the questions

 

[deelaw007]

Okay waut

 

[deelaw007]

Q6,8,10,15,16,17,21

 

[Eugene99]

Q6,8,10,15,16,17,21

my god! pity me! aren't they a lot?

 

[deelaw007]

come on

 

[Eugene99]

A'right
Q6:
a)
Using the 1st "2":
2,2: mean = 2
2,4: mean = 3
2,4: mean = 3
2,8: mean = 5
----------------------
Using the 2nd "2":
2,2: mean = 2
2,4: mean = 3
2,4: mean = 3
2,8: mean = 5
----------------------
Using the 1st "4":
4,2: = 3
4,2: = 38,2
4,4: = 4
4,8: = 6
-------------
Using the 2nd "4:
4,2: = 3
4,2: = 3
4,4: = 4
4,8: = 6
------------
Using the "8":
8,2: = 5
8,2: = 5
8,4: = 6
8,4: = 6

b)
Find the mean of {2,3,3,5,2,3,3,5,3,3,4,6,3,3,4,6,5,5,6,6}
= (13+13+16+16+22)/20 = (26+32+22)/20 = 80/20 = 4
----------
compute the population mean
Find the mean of {2,2,4,4,and 8} = 20/5 = 4
. compare the two values.
The mean of the sample means is the same as the mean of the population.
-----------------------------

c)
Range of the population is 8-2 = 6
Range of the sample means is 6-2 = 4
The sample means are less dispersed than the population.

 

[Eugene99]

Q8:
a)
Possible Samples:
0 0 1 mean = 1/3
0 0 3 mean = 1
0 0 6 mean = 3
0 3 6 mean = 3
0 1 3 mean = 4/3
0 1 6 mean = 7/3
1 3 6 mean = 10/3

b)
(1/3 + 1 + 3 + 4/3 + 3 +7/3 + 10/3) / 7

and the population mean
0, 0, 1, 3, 6 mean is 10/5 = 2

c)
Compare the two values

 

[Eugene99]

Q10:
a)
5C2 = 10
ten random samples

b)
(8,6), (8,4), (8,10), (8,6)
(6,4), (6,10), (6,6),
(4,10), (4,6)
(10,6)


means:
ẋ(8,6) = 7, ẋ(8,4) = 6, ẋ(8,10) = 9 , ẋ(8,6) = 7,
ẋ(6,4) = 5, ẋ(6,10) = 8, ẋ(6,6) = 6,
ẋ(4,10) = 7, ẋ(4,6) = 5,
ẋ(10,6) = 8

c) pop. mean & st. deviation
μ = (8 + 6 + 4 + 10 + 6)/5 = 6.8

mean X, of sample means (sampling distribution)
ẋ | P(ẋ)
```````````
5 | 2/10
6 | 2/10
7 | 3/10
8 | 2/10
9 | 1/10

X = sum of (ẋ P(ẋ) ) = 5(2/10) + 6(2/10) + 7(3/10) + 8(2/10) + 9(1/10)
X = 6.8
X = µ
mean of samples means is the same as population mean

d)
pop st. deviation
σ = √ [ { (6.8-8)²+(6.8-6)²+(6.8-4)²+(6.8-10)²+(6....‡ } / 5 ] = 2.04

sample deviation, s
s² = Σ(x - µ)²/(n - 1)
s² = [ (7-6.8)² + (6-6.8)² + (9-6.8)² + (7-6.8)² + (5-6.8)² + (8-6.8)² + (6-6.8)² + (7-6.8)² + (5-6.8)² + (8 -6.8)² ] /(10 - 1)
s² = 1.7333
s = 1.32
s < σ
dispersion in sample means is smaller than that of the population