Question

How will decreasing the level of confidence without changing the sample size affect the width of a confidence interval for a population mean? Assume that the population standard deviation is unknown and the population distribution is approximately normal

Answer 1

Without changing the sample size the change of CI may affect the results

Explanation:

According to Central Limit theorem the sampling distribution is given by

Z= x`- u/ σ/√n

Z has in the limit a standard normal distribution and

x`= u ± zσ/√n

From the above

x`- z∝(σ/√n) ≤ u ≤ x`+ z∝(σ/√n)

This formula is used for the confidence interval with normal population and unknown standard deviation.

But if the different values of Z∝ are used the results will be different.

If the CI of 99% or 95% or 90% is used the values of acceptance and rejection regions change and therefore the results will change.

The value of Z∝ for

∝= 0.1 is ± 1.645

∝= 0.05 is ± 1.96

∝= 0.01 is ± 2.58

Suppose we get the calculated Z value equal 2.59 but we decrease the CI from 0.05 to 0.01 the acceptance region would become rejection region and the level of confidence will change.