SOLUTION: Construct the indicated confidence interval for the population mean μ using the​ t-distribution. Assume the population is normally distributed. c=0.90​, x=13.5​, s=0.77â€

Algebra ->  Probability-and-statistics -> SOLUTION: Construct the indicated confidence interval for the population mean μ using the​ t-distribution. Assume the population is normally distributed. c=0.90​, x=13.5​, s=0.77†     Log On


   

Question 1204517: Construct the indicated confidence interval for the population mean μ using the​ t-distribution. Assume the population is normally distributed.
c=0.90​, x=13.5​, s=0.77​, n=15
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The formula for estimation is:
mu+=+M+%2B-+t%28s%5BM%5D%29

where:
M = sample mean
t = t statistic determined by confidence level
s%5BM+%5D= standard error = sqrt%28s%5E2%2Fn%29
given
M=+13.5
n=15
s=0.77
c=+0.90

A 90% Confidence Interval will have the same critical values (rejection regions) as a two-tailed z test with alpha+=+.10.

zc-CI90-Table-1024x426

so, z-score for 90% confidence interval is ±1.6445



mu+=+M+%2B-+t%28s%5BM%5D%29
mu+=+M+%2B-+t%28sqrt%28s%5E2%2Fn%29%29
mu+=13.5+%2B-+1.6445sqrt%280.77%5E2%2F15%29
mu+=+13.5+%2B-+0.326948217125689

90% confidence interval is [13.17, 13.83]
You can be 90% confident that the population mean (mu) falls between 13.17 and 13.83.