Let's approach a problem from two perspectives: An engineer believes a particular component has a fatigue life of 10000. In other words, that component should be expected to fail after 10000 uses. He takes a random sample of 38 components and obtains a sample mean of 9900 with a standard deviation of 2250. Is there any evidence that he is overestimating the fatigue life of the components? What is the value of the test statistic? What is the p-value for his test? Now let's examine the problem from another perspective: A particular component has a fatigue life of 10000. An engineer took a random sample of 38 components and tested their fatigue. He obtained a sample mean of 9900 cycles with a standard deviation of 2250. Notice that the standard deviation comes from the sample, so a t distribution would be appropriate to use here. (d) What is the center of the sampling distribution? (e) How many standard errors from the center of the sampling distribution did the sample mean fall? Use a negative sign if it fell below the center. (3 decimal places) (f) What was the probability of obtaining a sample mean of 9900 or less? (3 decimal places) What could we say about the answers to (c) and (f)? 1. They should be different. 2. They are unrelated. 3. They should be the same..

1. Let's approach a problem from two perspectives:
An engineer believes a particular component has a fatigue life of 10000. In other words, that
component should be expected to fail after 10000 uses. He takes a random sample of 38
components and obtains a sample mean of 9900 with a standard deviation of 2250. Is there any
evidence that he is overestimating the fatigue life of the components?
What is the value of the test statistic?
What is the p-value for his test?
Now let's examine the problem from another perspective:
A particular component has a fatigue life of 10000. An engineer took a random sample of 38
components and tested their fatigue. He obtained a sample mean of 9900 cycles with a standard
deviation of 2250. Notice that the standard deviation comes from the sample, so a t distribution
would be appropriate to use here.
(d) What is the center of the sampling distribution?
(e) How many standard errors from the center of the sampling distribution did the sample mean
fall? Use a negative sign if it fell below the center. (3 decimal places)
(f) What was the probability of obtaining a sample mean of 9900 or less? (3 decimal places)
What could we say about the answers to (c) and (f)?
1. They should be different.
2. They are unrelated.
3. They should be the same.