Looking at my answers, I was am always off buy about range of .1
to .4 from the correct answer that is stated. I am having a really
tough time trying to figure out how to get my number to be exactly
like what is shown as correct so I need a little help with figuring
out what I am doing wrong. Here is an example of a question I just
cant seem to figure out. I'll show all my steps and let me know
what I am doing wrong please
Construct a 90% confidence interval to estimate the population mean using the data below.
x̅ =50 σ=10 n=20 N=200
The 90% confidence interval for the population mean is (___, ___)
(Round to two decimal places as needed.)
UCLx̅ = x̅ + (critical z-value)(σx̅)
LCLx̅ = x̅ - (critical z-value)(σx̅)
So I find σx̅
σx̅ = σ/√n σx̅ = 10/√20 = 2.236
Finding Critical z - value
α = (1 - confidence interval) then divide by 2 (1 - .90)/2 = .05 then using technology I find the z-value of .05 = 1.645
Plug it all in
50 + (1.645)(2.236) = 53.68
50 - (1.645)(2.236) = 46.32
I then have an answer that the 90% confidence interval for the population mean is (46.32, 53.68) which is incorrect. The correct answer shown is (46.50, 53.50) but I am unsure how to get this interval. Could someone work this out and show me the steps on how to get the correct interval please?
Note: The 90% confidence interval is (46.3217 , 53.6783) . Your answer and all the steps are correct. There may be some error in the given data or the answer.
We need to construct the 90% confidence interval for the population mean μ. The following information is provided:
x̅ =50, σ=10 and n=20
The critical value for α=0.1 is Zc=Z1−α/2 = 1.645. The corresponding confidence interval is computed as shown below:
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