The compressive strength of lunar concrete is being analyzed by acivil engineer.

Question

The compressive strength of lunar concrete is being analyzed by acivil engineer. The engineer tests a sample of eight specimens andobtains the following compressive strengths (in psi). (adapted from[Kiemele et al. 2000])

3850 3640 3720 3400 3350 3575 3500 3650

a. Create a 90% confidence interval for the compressive strength oflunar concrete.
b. Create a 95% confidence interval for the compressive strength oflunar concrete.
c. Create a 99% confidence interval for the compressive strength oflunar concrete.
d. Compare the results.

Explanation / Answer

sample mean, x = 3585.6 standard deviation, s = 165.82 sample size, n = 8 degree of freedom, df = n-1 = 8-1 =7 standard error, e = s/n = 165.82/8 = 58.63 a) at 90% confidence, i.e = 0.1, df = 7 and two taildistribution, t = 1.895 hence confidence interval = x ± t*e = 3585.6 ±(1.895*58.63) =(3474.5, 3696.7) b) at 95% confidence, i.e = 0.05, df = 7 and two taildistribution, t = 2.365 hence confidence interval = 3585.6 ±(2.365*58.63) =(3446.94, 3724.26) c) at 99% confidence i.e =0.01, df = 7 and two taildistribution, t = 3.499 confidence interval = 3585.6 ± (3.499*58.63) =(3380.45, 5790.75) d) as the confidence interval is increasing, the range of theconfidence interval is also increasing

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