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.

12.3	11.6	11.9	12.1	12.5	11.4	12.0
11.7	11.8	12.3

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

90% confidence interval:_____________ ≤ μ ≤ _____________
95% confidence interval: ____________ ≤ μ ≤ _____________l  
99% confidence interval: ____________ ≤ μ ≤ _____________

The point estimate is_________.

Answer 1

given data,

12.3	11.6	11.9	12.1	12.5	11.4	12.0
11.7	11.8	12.3

n = 10

sum = 119.60

mean = 11.96

var = 0.12

st dev = 0.35

we know that confidence interval is given by,

where, x = 11.96

t = 1.83 (t value at 90% confidence interval with DF = 10-1 = 9 is 1.83)

s = 0.35

n = 10

1) confidence interval at 90% confidence interval is,

= [11.76, 12.16]

2) confidence interval at 95% confidence interval is,

= [11.71, 12.21]

3) confidence interval at 99% confidence interval is,

= [11.60, 12.32]

Therefore,

90% confidence interval: 11.76 ≤ μ ≤ 12.16
95% confidence interval: 11.71 ≤ μ ≤ 12.21
99% confidence interval: 11.60 ≤ μ ≤ 12.32

The point estimate is 11.96