Question

Question 18 of 21 5 Points Suppose that two researches are constructing 95% confidence intervals as part of their different studies on consumer behavior. Researcher A has decided to randomly sample 100 consumers and Researcher B has decided to randomly sample 64 consumers. The standard deviation (0) for the variable which Researcher A is studying is known to be 5. The standard deviation (0) for the variable which Researcher B is studying is known to be 4. Which of the following statements is true? A. None of these answers are correct B. Both researcher's intervals have the same precision, but the confidence is different Ο Ο Ο Ο OC. Both researcher's intervals have the same confidence and the same precision D. Both researcher's intervals have the same confidence, Researcher B's interval has more precision O E. Both researcher's intervals have the same confidence, Researcher A's interval has more precision Reset Selection

Answer 1

As for both the researchers, the confidence interval is same as 95%. Hence for both the cases the confidence is same.

Now we know that precision of any estimation or prediction increases as the sample size increases and/or underlying population variance decreases. Now here we see that , the sample size for researcher A(=100) is more than that for B (= 64). But variance for A is less than B so precision can not be determined like this. Also here it is not clear that which is being estimated by this confidence interval.

So it is clear that precision is different for the two researchers but it is not clear who is more precise.

If it is for mean , then precision increases if sigma/√n decreases, where sigma is standard deviation and n is sample size.

For researcher A, sigma/√n = 5/√100=0.5

For researcher B, sigma/√n= 64/√4= 32

Hence precision is more for researcher A.

Hence confidence is same but precision is different and is more for A.

Answer: option E.

Hope the solution helps. Thank you.

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