Respuesta :
Answer:
The engineer who weighed the rod 25 times will have the narrower confidence interval.
Step-by-step explanation:
The confidence interval for a mean has a margin of error that depends on n.
This margin of error, that defines how narrower is the intervla, is calculated as:
[tex]MOE=z\cdot \dfrac{ \sigma}{\sqrt{n}}[/tex]
That means that increasing the sample size will decrease the margin of error and then make the confidence interval narrower.
The engineer who weighed the rod 25 times will have the narrower confidence interval.
Answer: 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.
