SOLUTION: Construct the confidence interval for the population mean u. c= 0.98, x =7.4, s =0.5, n= 60 985 confidence interval

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Question 1179142: Construct the confidence interval for the population mean u.
c= 0.98, x =7.4, s =0.5, n= 60
985 confidence interval

Found 2 solutions by Theo, ewatrrr:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i'm not quite sure if i understand fully what you want, but what i think is this.

the confidence level is .98.
the sample mean is 7.4
the population standard deviation is .5
the sample size is 60.

if we let m = the population mean, then the z-score formula says that.

z = (x - m) / s

z is the z-score.
x is the mean of the sample
m is the mean of the population
s is the standard error of the distribution of sample means.

the formula for s would be:

s = standard deviation of the population divided by the square root of the sample size.

that would make s equal to .5/sqrt(60) = .0645497224 = .06455 rounded to 5 decimal places.

the formula becomes:

z = (7.4 - m) / .06455

with two tailed confidence level of 98%, the alpha on each end would be .01.

you would be looking for a z-score that has .99 area to the left of it or .01 area to the left of it.

that would make the z-score plus or minus 2.326 rounded to 3 decimal places.

when the z-score is plus 2.326, the formula becomes 2.326 = (7.4 - m) / .06455
multiply both sides of this equation by .06455 to get:
2.326 * .06455 = 7.4 - m
add m to both sides of this equation and subtract 2.326 * .06455 from both sides of this equation to get:
m = 7.4 - 2.326 * .06455 which makes m = 7.2498567

when the z-score is minus 2.326, the formula becomes -2.326 = (7.4 - m) / .06455.
multiply both sides of this equation by .06455 to get:
-2.326 * .06455 = 7.4 - m
add m to both sides of this equation and add -2.326 * .06455 to both sides of this equation to get:
m = 7.4 + 2.326 * .06455 which makes m = 7.5501433.

at 98% confidence level, the true population mean is assumed to be somewhere between 7.2498567 and 7.5501433.

this is what the 98% confidence interval looks like.









Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
z+=blue+%28x+-+mu%29%2Fblue%28sigma%2Fsqrt%28n%29%29+=++ME%2Fblue%28sigma%2Fsqrt%28n%29%29}}}
ME+=+z%2Asigma%2Fsqrt%28n%29
c= 0.98, x =7.4, s =0.5, n= 60
ME = 2.326(.5)/sqrt(60) = .15
7.4 - .15 < mu < 7.4 + .15
CI: ( 7.25, 7.55)