Question

- In the 1940s, the U.S. Department of Commerce reported a new way to test the tensile
strength, in pounds per square inch, of concrete. Several samples of concrete specimens
were used to estimate the mean tensile strength of 430 pounds per square inch with a
margin of error of 10 pounds per square inch. After the study was published, another
group proposes to run the same test on concrete specimens but with samples including
many more concrete specimens in each sample. (2 points)
Which of these statements is most likely to be true about the second study?
A. The estimated mean will be greater than 440 pounds per square inch.
B. The margin of error for the second study will likely be around 10 pounds per square inch.
C. The margin of error for the second study will likely be greater than 10 pounds per square inch.
D. The margin of error for the second study will likely be less than 10 pounds per square inch.

Answer 1

Using the Central Limit Theorem, it is found that the statement that is likely to be true about the second study is given by:

D. The margin of error for the second study will likely be less than 10 pounds per square inch.

What does the Central Limit Theorem states?

It states that the sampling distribution of sample means of size n has standard error $s = \frac{\sigma}{\sqrt{n}}$.

That is, higher sample sizes leads to lower amounts of error, and since the second study has a higher sample size, it should have lower error, hence option D is correct.

More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213

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