Question

how do I solve the problem: Za/2 corresponds with a 85% CL

Answer 1

You need to find the value of k such that

P(Z < -k) = 0.075

This is because 85% (or 0.85) of the distribution is between -k and k. Where k is some positive number.

The remaining amount of the distribution, which is 100 - 85 = 15%, is divided equally between the tails. So each tail gets 15/2 = 7.5%

So that's how I got 0.075

Answer 2

Does that make sense?

Answer 3

Yes, it does! Now why couldn't my book explain it in layman's terms like that?! =) thank you!

Answer 4

you're welcome

Answer 5

Ok, so my HW says that's wrong..
looking for a level of confidence = (1-a) *100%
.85 = (1-a)*1

Answer 6

what did you get for that value of k

Answer 7

and if possible, post a screenshot of the entire problem please

Answer 8

I don't know how to do a screen shot..nor solve for K.

Answer 9

or how k ended up in the equation..

Answer 10

you hit print screen

open up MS paint

paste it in

save it, send it

Answer 11

'm using a mac

Answer 12

well k is an added variable

Answer 13

ok one sec

Answer 14

mac OS X right?

Answer 15

affirmative.

Answer 16

you hit

Command-Shift-3

that will save a PNG file to the desktop

Answer 17

the PNG file will be what you are currently looking at

Answer 18

ok you want to find the z score such that the area to the left of the z-score is 0.075

so if k is that z-score (adding this variable in)

then

P(Z < k) = 0.075

Answer 19

this part is what was found above

Answer 20

to find this value of k, you either use a table or a calculator

preferably, you can use a calculator

if you can, then this one is very handy

http://www.wolframalpha.com/input/?i=normalcdf&a=*C.normalcdf-_*Formula.dflt-&f2=0.075&x=3&y=4&f=NormalProbabilities.pr_0.075&a=*FVarOpt.1-_***NormalProbabilities.pr--.***NormalProbabilities.z--.**NormalProbabilities.l-.*NormalProbabilities.r---.*--&a=*FVarOpt.2-_**-.***NormalProbabilities.mu--.**NormalProbabilities.sigma---.**NormalProbabilities.pr---

Answer 21

or if you have a TI calculator, you can use the "invNorm" function and type in

invNorm(0.075)

to get -1.44 roughly

Answer 22

so

-k = -1.44

k = 1.44

Answer 23

Which means that the z critical value for the 85% confidence interval is roughly 1.44

Answer 24

where is the "invNorm" function roughly located on the TI calculator?

Answer 25

brb

Answer 26

hit

2nd key, then the VARS key

Answer 27

it's option #3

Answer 28

got it.

Answer 29

ok so you were able to get -1.44 or -1.439531471... right?

Answer 30

yes, which you divide by 1 to get the positive #?

Answer 31

or rather the -1

Answer 32

the positive version of that number is 1.439531471

so that's your z critical for the 85% CL

Answer 33

ha. that made since but I input the answer wrong again..and it gave me the correct answer as to being .15..did I need to move a decimal?

Answer 34

it says the answer is 0.15 ?

Answer 35

yes. I'll screen shot it.

Answer 36

ok thanks

Answer 37

oooh it wants the alpha value

Answer 38

if CL = 0.85

then

alpha = 1 - CL

alpha = 1 - 0.85

alpha = 0.15

Answer 39

but that's odd since you wanted the critical value first, but oh well

Answer 40

oooh.

Answer 41

oh you're still doing the example, I gotcha

Answer 42

sorry wasn't sure where you were at lol

Answer 43

that's ok. I'm not sure of that either. =)

Answer 44

but anyway on the main problem for #2, you find the alpha value (in this case 0.15)

and you use that to determine z(a/2) which is the critical value for the confidence interval

Answer 45

I'm sure that this example will have you using a table, but a calculator is quicker, easier, and more accurate

Answer 46

to my knowledge, no tables were provided..let me double check my book.

Answer 47

alright, tables might be provided in the front or back of the book

they also might be given out as extra stuff to download (or maybe given out as links)

Answer 48

I know I have a few tables in PDF form (just the tables themselves) on my computer when I took stats since the professor sent a few that way

Answer 49

nope, I don't see anything.

Answer 50

ok then maybe your teacher has posted the tables or has sent the tables in another form

Answer 51

sometimes, when doing a problem like this, the table will be given alongside the problem (like you click a button off to the side of the problem and the table used will pop up)

Answer 52

nope, no table provided. We had the answer but the question was breaking it down step by step..and I was jumping ahead. thank you for your assistance. I'm going to try another problem and see how it goes.

Answer 53

alright, well anyway, if you break from the example in #2

and go back to the main problem #2

the final answer should be 1.43953147, make sure you round this to whatever place they want

Answer 54

yes, I did..and it was correct - woohoo!

Answer 55

alright great lol