Question

Determine whether the given conditions justify using the margin of error E = z_/2 / when finding a confidence interval estimate of the population mean .

The sample size is n = 8,  = 12.1, and the original population is normally distributed.

Group of answer choices

Yes

No

Answer 1

We are given that original population is normally distributed.

We need to determine whether the given conditions justify using the margin of error E = z_/2 or not .

The sample size is n = 8,  = 12.1

Now if we are performing t-test , or finding confidence interval for population mean , then we need to estimate Margin of error E , assuming that the sample are approximately normaly distributed .

Here n = 8 ( less than 30 )

To use " z_/2 / " i.e z-score to estimate Margin of error E , we should have (i) Standard deviation of the population i.e Population Standard deviation should be known and (ii) sample size n should be more than 30 in order to be able to use the z-score .

Since here n = 8 , which is not sufficiently large sample size , so we cannot use z-score here , as both requirenment are not met

As z-score formula is applicable or more suitable if sample size n is more than or equal to 30 , otherwise we use t-score

Hence conditions do not justify .

Correct answer is :-

Q. Determine whether the given conditions justify using the margin of error E = z_/2 / when finding a confidence interval estimate of the population mean .

Ans No

( As sample size n=8 is not sufficiently large , hence conditions do not justify using the margin of error E = z_/2 / ,   so we can not use z-score . Hence it do not justify )