Statistical Inference

[Eugene99]

We go in the reverse order when we have the z value and we have to find x value. For example, when we are given mean, standard deviation and the X as well. Then, we see the z-value and see which x-value it corresponds to. You will see this in Q42. Here is how we solve it:

mean= 1994
sd = 450

a) X> 2500
2500-1994/ 450 = 1.12 : it's the z-value we have got
look for 1.1 in the z-values first then go till 2 from the top, we get 0.8686 for 1.12 (we did the reverse when we were finding z-value, this time we have the z-value so we simply look for the x-value) (all those in the middle are x-values, only the border upper and right lines are z-values)
So, over here, 0.8686
1 - 0.8686 ( we always subtract the z-value from 1 when we are finding X is greater than something)
=0.1314
which is 13.14%

 

[deelaw007]

and 28, 29 and 37

 

[Eugene99]

b) Between 2500 and 3000
2500-1994/450 < Z < 3000-1994/450 (It means nothing but just that we are finding values between 2500 and 3000, so on one side we find for 2500 and on the other for 3000)

1.12 < Z < 2.23
see values from the table, again we have z-values just see the corresponding x-values
at 1.12 its: 0.8686
at 2.23 it's: 0.9871

0.9871 - 0.8686
=0.1185
or 11.85%

 

[deelaw007]

b) Between 2500 and 3000
2500-1994/450 < Z < 3000-1994/450 (It means nothing but just that we are finding values between 2500 and 3000, so on one side we find for 2500 and on the other for 3000)

1.12 < Z < 2.23
see values from the table, again we have z-values just see the corresponding x-values
at 1.12 its: 0.8686
at 2.23 it's: 0.9871

0.9871 - 0.8686
=0.1185
or 11.85%

 

[deelaw007]

solwe those :3

 

[deelaw007]

and part c?

 

[Eugene99]

solwe those :3

yep doing
oh there is part c too?
wait a bit

 

[Eugene99]

yep doing
oh there is part c too?
wait a bit

you try part c, done the same way, it's just soo easy, give it a try, I'll post the solution then match

 

[deelaw007]

you try part c, done the same way, it's just soo easy, give it a try, I'll post the solution then match

Alrightt
There is another chapter
Sampling methods and the central limit theorem

 

[Eugene99]

Alrightt
There is another chapter
Sampling methods and the central limit theorem

I think that's in S2, I've just studied S1 yet for my AS

 

[deelaw007]

I think that's in S2, I've just studied S1 yet for my AS

Lol
part c do it now

 

[Eugene99]

Q42
c)
1000-1994/450
= -2.20
at 2.20 table shows: 0.9861 but that's for 2.20 not for -2.2, (when we get a negative value, we simply subtract the positive from 1 to get the negative, because we are only given positive values in the table in exam and not the negative)
so 1 - 0.9861 (for -2.20)
gives us 0.0139
Multiply that 100 to get percentage which is 1.39, round off to 1.4 %

 

[Eugene99]

Q28:
We get that damn z value again (will have to go in reverse order in table)
We are given mean, sd and the z-value, putting them into formula, we have:
0.95 = (X-26889/ 4500)
at 0.95, it's actually (0.9505 but it'll do) it comes under 1.6 from the right and in the 5 from the top
so,
1.65 = X-26889/4500
1.65 x 4500 = X -26889
7425+ 26889 = X
X= 34314

 

[Eugene99]

Q28:
We get that damn z value again (will have to go in reverse order in table)
We are given mean, sd and the z-value, putting them into formula, we have:
0.95 = (X-26889/ 4500)
at 0.95, it's actually (0.9505 but it'll do) it comes under 1.6 from the right and in the 5 from the top
so,
1.65 = X-26889/4500
1.65 x 4500 = X -26889
7425+ 26889 = X
X= 34314

I don't know if the answer is correct, without the answers, there is no certainty

 

[Eugene99]

Q28:
We get that damn z value again (will have to go in reverse order in table)
We are given mean, sd and the z-value, putting them into formula, we have:
0.95 = (X-26889/ 4500)
at 0.95, it's actually (0.9505 but it'll do) it comes under 1.6 from the right and in the 5 from the top
so,
1.65 = X-26889/4500
1.65 x 4500 = X -26889
7425+ 26889 = X
X= 34314

Okay see, if we want an ACCURATE answer, instead of taking 1.65 which corresponds to 0.9505, we can take 1.645 that will mean between 1.64 and 1.65, and it will be correct because our value of 0.95 lies in the middle of 0.9495 and 0.9505, so 1.645 will get us a more correct answer

 

[deelaw007]

Q42
c)
1000-1994/450
= -2.20
at 2.20 table shows: 0.9861 but that's for 2.20 not for -2.2, (when we get a negative value, we simply subtract the positive from 1 to get the negative, because we are only given positive values in the table in exam and not the negative)
so 1 - 0.9861 (for -2.20)
gives us 0.0139
Multiply that 100 to get percentage which is 1.39, round off to 1.4 %

on -2.2 Im getthe the exact walue 0.0139 in the table

 

[deelaw007]

Q42
c)
1000-1994/450
= -2.20
at 2.20 table shows: 0.9861 but that's for 2.20 not for -2.2, (when we get a negative value, we simply subtract the positive from 1 to get the negative, because we are only given positive values in the table in exam and not the negative)
so 1 - 0.9861 (for -2.20)
gives us 0.0139
Multiply that 100 to get percentage which is 1.39, round off to 1.4 %

I hawe the negatiwe ones

 

[Eugene99]

I hawe the negatiwe ones

but you have to see if they give you negative ones in exam or not so prepare accordingly
We don't get negative values

 

[deelaw007]

but you have to see if they give you negative ones in exam or not so prepare accordingly
We don't get negative values

then why we subtract 1 in part a?

 

[Eugene99]

then why we subtract 1 in part a?

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?