The American Banking Association (ABA) surveyed 110 banks and found the sample h

Question

The American Banking Association (ABA) surveyed 110 banks and found the sample had mean assets of 220 million dollars. The sample standard deviation of their assets was 161 million dollars. Give a 98% confidence interval for , the mean assets for all community banks (in millions of dollars). Put the lower bound in Answer 1 and the upper bound in Answer 2.
Suppose the ABA sampled 150 banks, and found the same sample mean and sample standard deviation. Give a 98% confidence interval for the population mean. Put the lower bound in Answer 3 and the upper bound in Answer 4.


1.
2.
3.
4.

and

Which statement is true? The 95% confidence interval is wider than the 90% confidence interval because
A. The standard error for the 95% interval is bigger than for the 90% interval.
B. we can only be more confident in the estimate if we include more possible values for the population mean.
C. the margin of error for the 90% interval is bigger than for the 95% interval.
D. there's a higher probability of 95% confidence interval containing the mean than the 90% confidence interval containing the mean.

i know its not d/b but i cant figure out between a or c.

please give explanations.

Thanks

Explanation / Answer

A. The standard error for the 95% interval is bigger than for the 90% interval. The standard error for 95% has a larger interval because we are 95% confident that the true mean lies in the interval. Because we are more confident, the interval needs to bigger. Therefore, A is true.

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