In a study of the lifetimes of electronic components
12. In a study of the lifetimes of electronic components, a random sample of 400 components are tested until they fail to function. The sample mean lifetime was 370 hours and the standard deviation was 650 hours. True or false:
a. An approximate 95% confidence interval for the mean lifetime of this type of component is from
306.3 to 433.7 hours.
b. About 95% of the sample components had life- times between 306.3 and 433.7 hours.
c. If someone takes a random sample of 400 components, divides the sample standard deviation of their lifetimes by 20, and then adds and sub- tracts that quantity from the sample mean, there is about a 68% chance that the interval so con- structed will cover the mean lifetime of this type of component.
d. The z table can’t be used to construct confidence intervals here, because the lifetimes of the compo-
ii. one-fourth as wide
iii. one-half as wide
iv. the same width
v. twice as wide
vi. four times as wide
vii. eight times as wide