Question

: A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 45 cables and apply weights to each of them until they break. The mean breaking weight for the 45 cables is 768.2 lb. The standard deviation of the breaking weight for the sample is 15.1 lb. Using the sample information as given, construct a confidence interval for the mean breaking strength of the new steel cable.

if a 95% level of confidence is applied, the interval estimate is: a. (763.788, 772.612) in ounces

b. (762.402, 773.998) in kilograms

c. (764.497, 771.903) in pounds

d. (763.788, 772.612) in pounds

The proper interpretation of the interval estimate in #1is:

a. With a 95% level of confidence, the breaking strength of the new steel

cable falls between 763.788 pounds and 772.612 pounds.

b. With a 95% level of confidence, the average breaking strength of the new steel cable falls between 763.788 pounds and 772.612 pounds.

c. With a 95% level of confidence, each of the new steel cable has a breaking

strength of 772 pounds.

d. With a 95% level of confidence, the average breaking strength of the new

steel cable falls between 764.497 pounds and 771.903 pounds.

Answer 1

Ans. Option d

Mean breaking weight, x = 762.8 lb

Standard deviation, s = 15.1 lb

Sample size, n = 45 cables

Standard error, se = s/n0.5 = 2.25 lb

Z at level of significance 5% = +-1.96

95% confidence interval of mean breaking weight,

CI = [x - z*se, x + z*se] = [762.8 - 1.96*2.25, 762.8 + 1.96*2.25] = [763.788, 772.612] in pounds

Ans. Option b

With 95% level of confidence, the average breaking strength is of the new steel cable falls between 763.788 pounds and 772.612 pounds.

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