Question

How would the 95% confidence interval be affected if we had a larger sample size with around the same standard
deviation?


Select the single best answer:
A Narrower
B. Larger
C. Remain the same​

Answer 1

Answer:

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Answer 2

You can compute a confidence interval (CI) for a population's mean, or average, if you know the standard deviation. When evaluating a numerical statistical characteristic, most people want to know what the population's mean (average) value is.

Using a sample mean, x, plus or minus a margin of error, you estimate the population mean. The result is known as a confidence interval for the population mean, or a confidence interval for the population mean.

∴ Confidence Interval  = x ± z* $\frac{\alpha }{\sqrt{n} }$

∴ If a larger sample size is taken, n increases.

∴ √n increases.

∴  $\frac{\alpha }{\sqrt{n} }$ decreases.

∴ The confidence interval narrows.

∴ (a) Narrower