Length of a rod: Engineers on the Bay Bridge are measuring tower rods to find out if any rods have been corroded from salt water. There are rods on the east and west sides of the bridge span. One engineer plans to measure the length of an eastern rod 25 times and then calculate the average of the 25 measurements to estimate the true length of the eastern rod. A different engineer plans to measure the length of a western rod 20 times and then calculate the average of the 20 measurements to estimate the true length of the western rod. Suppose the engineers construct a 90% confidence interval for the true length of their rods. Whose interval do you expect to be more precise (narrower)? Group of answer choices Both confidence intervals would be equally precise. The engineer who weighed the rod 25 times. The engineer who weighed the rod 20 times.

The engineer who weighed the rod 25 times.

Step-by-step explanation:

In both scenarios, the samples are lesser than 30, so the t distribution would be used.

Confidence interval = sample mean ± margin of error

Margin of error = t score × sample standard deviation/√number of samples

How narrow the confidence interval is depends on the margin of error contained in the confidence interval. The margin of error also depends on the number of samples as well as the confidence level. Since the confidence level is the same for both measurements, we would compare for both scenarios.

For the engineer who plans to measure the length of an eastern rod 25 times and then calculate the average of the 25 measurements, we would determine the t score from the t distribution table.

Degree of freedom = 25 - 1 = 24

t score = 1.711

For the engineer who plans to measure the length of a western rod 20 times and then calculate the average of the 20 measurements,

Degree of freedom = 20 - 1 = 19

t score = 1.729

The scenario with higher number of samples gave a lower t score and it will also give a narrower confidence interval. Therefore, the more precise or narrower confidence interval would be

The engineer who weighed the rod 25 times.

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step-by-step explanation:

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