Problem 11E

The length of a rod was measured eight times. The measurements in centimeters, in the order they were taken, were 21.20, 21.22, 21.25, 21.26, 21.28, 21.30, 21.32, 21.35.

a. Do these measurements appear to be a random sample from a population of possible measurements? Why or why not?

b. Is it possible to estimate the uncertainty in these measurements? Explain.

Solution 11E

Step1 of 3:

Let us consider a variable X it presents length of the rod was measured eight times And this length is measured in cm’s.

X |
21.2 |
21.22 |
21.25 |
21.26 |
21.28 |
21.3 |
21.32 |
21.35 |

Here our goal is:

a).We need to check is these measurements appear to be a random sample from a population of possible measurements? Why or why not?

b).We need to check Is it possible to estimate the uncertainty in these measurements? Explain.

Step2 of 3:

a).

No, These measurements appear to be a random sample from a population of possible measurements because, the given measurements of length of rod is in increasing order and these measurements would be highly unusual for a simple random sample.

Step3 of 3:

b).

No, It is not possible to estimate the uncertainty in these measurements because, from part (a) we have seen that measurements would be highly unusual for a simple random sample. Hence, we cannot estimate the uncertainty.