Introduction to Probability and Statistics for Engineers and Scientists

Problems 285

6.68 6.66 6.62 6.72

6.76 6.67 6.70 6.72

6.78 6.66 6.76 6.72

6.76 6.70 6.76 6.76

6.74 6.74 6.81 6.66

6.64 6.79 6.72 6.82

6.81 6.77 6.60 6.72

6.74 6.70 6.64 6.78

6.70 6.70 6.75 6.79

Assume a normal population.

38.The following are independent samples from two normal populations, both of

which have the same standard deviationσ.

16, 17, 19, 20, 18 and 3, 4, 8

Use them to estimateσ.

39.The amount of beryllium in a substance is often determined by the use of a

photometric filtration method. If the weight of the beryllium isμ, then the

value given by the photometric filtration method is normally distributed with

meanμand standard deviationσ. A total of eight independent measurements of

3.180 mg of beryllium gave the following results.

3.166, 3.192, 3.175, 3.180, 3.182, 3.171, 3.184, 3.177

Use the preceding data to

(a) estimateσ;

(b) find a 90 percent confidence interval estimate ofσ.

40.IfX 1 ,...,Xnis a sample from a normal population, explain how to obtain a

100(1−α) percent confidence interval for the population varianceσ^2 when the

population meanμis known. Explain in what sense knowledge ofμimproves the

interval estimator compared with when it is unknown.

Repeat Problem 38 if it is known that the mean burning time is 53.6 seconds.

41.A civil engineer wishes to measure the compressive strength of two different

types of concrete. A random sample of 10 specimens of the first type yielded

the following data (in psi)

Type 1: 3,250, 3,268, 4,302, 3,184, 3,266

3,297, 3,332, 3,502, 3,064, 3,116