Question

A random sample of 140 students is chosen from a population of 3,500 students. If the mean IQ in the sample is 105 with a standard deviation of 9, what is the 95% confidence interval for the students' mean IQ score?

a 100−120

b107.9−112.1

c 103.5−106.5

d108.66−111.34

Answer 1

you want a 95% confidence interval, right?

Answer 2

yes @abrahamglasser

Answer 3

so the right side will be at .975 and the left side will be at .025
1=.95 = .05
.05 / 2 = .025 (you are taking off .025 off each side to get the interval)
.95+.975

0+ .025 = .025

so the z scores are .025 and .975. do you know how to do the rest of it?

Answer 4

I have no idea how to do the rest of it :/

Answer 5

\[z = \frac{ x - \mu }{ \sigma }\]
mu is the mean and sigma is the standard deviation
now to find the interval
\[.025 = \frac{ x - 105 }{ 9 }\]
solve for x and that gives you the left side of the interval.
now the right side
\[.975 = \frac{ x - 105 }{ 9 }\]
solve for x and that gives you the right side of the interval.
these x's give you the answer

Answer 6

tell me if you dont understand something or if you dont know where i got these values, etc

Answer 7

wait, i think i made a mistake somewhere...

Answer 8

yea the answers weren't coming out right
for the right one I got 15.225

Answer 9

105.225*

Answer 10

i have to think about it...

Answer 11

ok

Answer 12

ok got it

Answer 13

i was thinking of a different confidence interval :(
sorry about that

Answer 14

ok, so the formula is..\[CI = x \pm Z _{\alpha/2}\times (\sigma/\sqrt n)\]
x = Mean
σ = Standard Deviation
α = 1 - (Confidence Level/100)
Zα/2 = Z-table value
CI = Confidence Interval

Answer 15

so it is \[105 \pm Z_{.025} * (9/ \sqrt 140)\]

Answer 16

and the z score of .025 is 1.96

Answer 17

ok so what do I do with the z score?

Answer 18

did you see the formula above it?

Answer 19

so it is
105±1.96∗(9/1√40)

Answer 20

i mean 105±1.96∗(9/√40)

Answer 21

that doesn't get me my answer what else do I have to do with that?

Answer 22

it doesn't? hmm.

Answer 23

none of my answer choices.

Answer 24

im pretty sure the actual answer is C) 103.5 - 106.5
i dont know why i keep getting different answers...

Answer 25

That's what I put down to begin with. This whole Exam is so weird. I don't understand it.

Answer 26

lol neither do i :P

Answer 27

although im pretty sure it's the right formula..

Answer 28

whatever. statistics is weird

Answer 29

Thank you so much for helping me. And I think it is. It looks really familiar.

Answer 30

no problem

Answer 31

Thankyou sooo muchh- this was correct!