Answer the following statement(s) true (T) or false (F)

Question

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.

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 lifetimes 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 subtracts that quantity from the sample mean, there is about a 68% chance that the interval so constructed 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 components don’t follow the normal curve.
e. About 68% of the components had lifetimes in the interval 370 ± 650 hours.

Answer 1

(a) True. A 95% confidence interval is found by adding and subtracting from the mean of 370.

(b) False. The confidence interval specifies the location of the population mean. It does not specify the proportion of the sample items that fall into any given interval.

(c) True. This describes the method to compute a 68% confidence interval, and this method produces an interval that covers the true value 68% of the times that it is used.

(d) False. So long as the sample mean is approximately normal, which will be the case when the sample is large, the method can be used.

(e) False. The confidence interval specifies the location of the population mean. It does not specify the proportion of the population that falls into any given interval.