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attashe74 [19]
3 years ago
12

We are to estimate the confidence interval for a population proportion p, based on two samples A and B of sizes 100 and 200, res

pectively. Both samples have the same standard deviations. Compare the lengths of the 95% confidence interval based on A to the interval based on B.
A. The length of the confidence interval based on A is the same as the length of the confidence interval based on B since the standard deviations for both samples are the same.
B. The length of the confidence interval based on A is larger than the length of the confidence interval based on B since SE for the sample A is larger than SE for the sample
C. The length of the confidence interval based on A is larger than the length of the confidence interval based on B since SE for the sample A is less than SE for the sample B.
D. The length of the confidence interval based on A is less than the length of the confidence interval based on B since SE of the sample A is larger than SE of the sample B.
E. The length of the confidence interval based on A is less than the length of the confidence interval based on B since SE of the sample A is less than the size of the sample B.
Mathematics
1 answer:
WITCHER [35]3 years ago
7 0

Answer:

The option B is True

Step-by-step explanation:

Solution

nA  < nB

Thus

1/√nA > 1/√nB

SD/√nA  > SD/√nB

So,

SE (A) > SE (B).......(1)

Zα/2 SE (A) > Zα/2 SE (B)

Now

E (A) > E(B)  this is the margin error

Since SE fro sample A is larger than SE for sample B

We have that,

The length = ZE

Therefore, option B is correct because here, we know that as the sample size increases or goes higher  the length of the confidence interval decreases

In this case, the  sample size is large for B then A.

Thus, the length of confidence interval based on A is larger than the length of confidence interval Based on B Since SE is large For A than B

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