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

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

Step-by-step 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.

answer: 2530

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