1.- The state auditor wants to find the average salary for...

1.- The state auditor wants to find the average salary for California City, California. A sample of 169 city employees yields a mean of $3000 per month. It is known that the standard deviation is $400. Find (a) a 90 percent confidence interval for the true mean salary. (b) a 90 percent confidence interval for the true mean salary. (b) a 99 percent confidence interval for the true mean salary. (d) How large of a sample is needed in order to have a margin of error of $200?

Transcript

00:01 I'll help you get set up on these.

00:01 I won't do all the calculations, but you start out with a sample size of 169, and you have that your sample mean is 3 ,000, and your population standard deviation is 400.

00:14 And on part a, you ask for a 90 % confidence interval for the mean.

00:19 And so that will be the 3 ,000 plus or minus, and we use a z value because this is known, and you would use 1 .645, and then times the standard.

00:30 Standard deviation over the square root of n.

00:33 And then you will do your calculation to get those values.

00:37 Now, b says the same thing.

00:39 I'm going to guess maybe you wanted a 95 % confidence interval.

00:43 And the only thing that will change is this value would become 1 .96.

00:48 And for part c, then you ask for a 99 % confidence interval.

00:55 And then the only thing that's going to change is this value will become 2 .576.

01:00 And you can find that.

01:02 And you can find the two values very easily with your calculator.

01:05 Then you've said in part d, and i have to see what you said, the margin of air or the percent.

01:12 Well, it says how large a sample size is needed in order to have the margin of air be 200? well, that's going to depend on your level of confidence.

01:21 So this is your margin of air, and you want that to equal, let me find it, 200.

01:31 And we know the population standard deviation is 400.

01:36 So you can substitute this value in as 400.

01:40 But i don't know what your level of confidence is.

01:44 And when you end up solving for n, you'll end up having n, the square root of n is equal to whatever the z value is for the level of confidence times 200, 400 divided by 200.

01:57 So that's going to end up being two.

01:58 So n will end up being that z value for whatever level you need times two quantity squared.

02:06 And then you will round that value up.

02:08 So again, i don't know which level of confidence.

02:11 And you can make a suggestion as to what it will be.

02:15 Now for your second one, you're dealing with proportions...

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