Question

A simple random sample of size n is drawn from a population that is known o be normally distributed. The sample mean xbar is 54.8. Construct a 90% confidence interval for the population mean if the population standard deviation is 10.5 and n = 20. I'm having trouble getting the Z-score because it asks for x and mu, neither of which I have? Or am I doing this totally wrong.

Answer 1

the standard deviation of the sample mean is the population std dev divided by sqrt(num samples)

Answer 2

Sooo... 10.5/20?

Answer 3

sqrt(20), not 20

Answer 4

Oh, right.

Answer 5

2.34

Answer 6

anyway then you use your handy z-table to find out what the z-value of 0.90 is

Answer 7

let's say (for the sake of argument) that it's 2. that means your 90% conf int would be 2 std devs above and below the mean. So you multiply the sample std dev by 2, and add (and subtract) that from the population mean to find the 90% conf int.

Answer 8

.9904

Answer 9

ah, you're using it backwards for this problem. you want to find an entry in the table that's 0.90 (or as close as possible) and find the corresponding z- value.

Answer 10

Ohh statistics, why are you so complicated.

Answer 11

statistics: why u no be easy??

Answer 12

Exactly! :C

Okay the closest I can find is 1.28 which is .8997

Answer 13

oh wait, i messed this up. that's the chance that 90% is below and 10% is above, but when you combine it with the 10% on the low side it's an 80% conf interval instead of a 90%.

So you need to exclude only 5% from the top, and 5% from the bottom to get a 90% conf interval. That means find 0.95 in the table (and 0.05, which will just be 1 - the 0.95 value)

Answer 14

..alright, I'll try that.

Answer 15

Anyway so you'll find that z-value. I think it's 1.64. Multiply that by the sample std dev you computed (std dev / sqrt(n)). Then add and subtract that from the sample mean and its your 90% conf int.

Answer 16

Alright, thanks.

I feel a bit dumb right now because at the bottom of the page it's got the numbers for conf int.s like 90% and 95%, so I probably could have done this on my own.

Answer 17

Oooh well.

Answer 18

what numbers do you mean? the z-score numbers?

Answer 19

Well it's got some common confidence interval numbers for quick reference.

b) Confidence Interval
Critical Values/ z«/2
Level of Confidence
0.90 or 90%
0.95 or 95%
0.98 or 98%
0.99 or 99%
Critical Value, zan
1.645
1.96
2.33
2.575

Answer 20

ah yes there's the 1.64 i said earlier

Answer 21

so that means your 90% conf int is plus or minus 1.645 std deviations above or below the mean. Std dev of your sample is pop std dev divided by sqrt(size of sample). Bang, done.

Answer 22

Yep, I got it :3