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 12.9 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: enter the lower limit of the 90% confidence interval ≤ μ ≤ enter the upper limit of the 90% confidence interval 95% confidence interval: enter the lower limit of the 95% confidence interval ≤ μ ≤ enter the upper limit of the 95% confidence interval 99% confidence interval: enter the lower limit of the 99% confidence interval ≤ μ ≤ enter the upper limit of the 99% confidence interval The point estimate is enter the point estimate .

Answer 1

Answers to questions asked:

90% confidence interval: 11.78 < < 12.31

95% confidence interval: 11.71 < < 12.37

99% confidence interval: 11.57 < < 12.51

The point estimate is 12.04

Explanation:

(i)

From the given data, the following statistics are calculated:

n = 10

= 12.04

s = 0.4575

= 0.10

df = 10 - 1 = 9

From Table, critical values of t = 1.833

90% Confidence Interval:

So,

Answer is:

(11.78, 12.31)

(ii)

From the given data, the following statistics are calculated:

n = 10

= 12.04

s = 0.4575

= 0.05

df = 10 - 1 = 9

From Table, critical values of t = 2.262

95% Confidence Interval:

So,

Answer is:

(11.71, 12.37)

(iii)

From the given data, the following statistics are calculated:

n = 10

= 12.04

s = 0.4575

= 0.01

df = 10 - 1 = 9

From Table, critical values of t = 3.25

99% Confidence Interval:

So,

Answer is:

(11.57, 12.51)