Question 980616: Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume
that the population has a normal distribution.
n = 10, x = 8.1, s = 4.8, 95% confidence
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume
that the population has a normal distribution.
n = 10, x-bar = 8.1, s = 4.8, 95% confidence
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Confidence Interval:: x-bar - ME < u < x-bar + ME
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ME = 1.96*4.8/sqrt(10) = 2.975
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95%CI: 8.1-2.98 < u < 8.1+2.98
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Ans: 5.12 < u < 11.08
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Cheers,
Stan H.
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Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website! xbar = 8.1
n = 10
s = 4.8
Since n = 10 makes n > 30 false, and because sigma is not known, we use a T distribution. The critical t value is t = 2.262 (at 95% confidence, df = n-1 = 10-1 = 9). Use a table to find this
The confidence interval is of the form (L,U) where L is the lower limit and U is the upper limit.
Lower Limit (L):
L = xbar - t*s/sqrt(n)
L = 8.1 - 2.262*4.8/sqrt(10)
L = 8.1 - 2.262*1.51789327688082
L = 8.1 - 3.43347459230442
L = 4.66652540769558
L = 4.67
Upper Limit (U):
U = xbar + t*s/sqrt(n)
U = 8.1 + 2.262*4.8/sqrt(10)
U = 8.1 + 2.262*1.51789327688082
U = 8.1 + 3.43347459230442
U = 11.5334745923044
U = 11.53
The 95% confidence interval for mu is (L,U) = (4.67, 11.53)
Note: The confidence interval can also be stated as 4.67 < mu < 11.53. Some books will use plus/minus notation and say  where 8.1 is the point estimate (xbar) and 3.43347 is the margin of error.
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