Question

Construct 90%, 95%, and 99% confidence intervals to estimate μ from the following data. State the point estimate. Assume the data come from a normally distributed population.

13.4 11.6 11.9 12.9 12.5 11.4 12.0 11.7 11.8 13.4

(Round the intermediate values to 4 decimal places. Round your answers to 2 decimal places.)

90% confidence interval: ______ ≤ μ ≤ ______

95% confidence interval: ______ ≤ μ ≤ ______

99% confidence interval: ______ ≤ μ ≤ ______

The point estimate is enter the point estimate _____

Answer 1

12.2600	mean Data
0.7427	std. dev.

Part a)

Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.1 /2, 10- 1 ) = 1.833

90% confidence interval is ( 11.83 , 12.69 )

part b)

Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.05 /2, 10- 1 ) = 2.262

95% confidence interval is ( 11.73 , 12.79 )

Part c)

Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.01 /2, 10- 1 ) = 3.250

99% confidence interval is ( 11.50 , 13.02 )

Point estimate = X̅ = 0.74