Question

An engineer has carefully measured the spacing between anchor bolts (in mm) as:

19          23          21            21
19          13          26            15
30          30          17            24
20          16          24            20

Find:
a. The 90 percent CI for µ
b. The 80 percent CI for µ
c. The 99 percent CI for µ assuming σ = 4.1 mm is known.

Answer 1

We have for given sample here,

Sample size:16

Mean (x̄): 21.125

Standard deviation (s): 4.8973

a) t critical value for 90% confidence level with degree of freedom =n-1=15 is 1.7531 (by using t table)

We are 90% confident that population mean is between 18.98 mm to 23.27 mm

b) t critical value for 80% confidence level with degree of freedom =n-1=15 is 1.3406 (by using t table)

We are 80% confident that population mean is between 19.48 mm to 22.77 mm

c) Z critical value for 99% confidence interval is 2.58(by using Z table)

We are 99% confident that population mean is between 18.48 mm to 23.77 mm