Question

In which of the following cases would it not be appropriate to use ?t procedures to make inferences about ?μ using ?¯x¯ ?

We have a sample of size ?=20 and x has a right‑skewed distribution with an outlier.

We have a sample of size ?=8 and x has a Normal distribution.

We have a sample of size ?=60 and x has a right‑skewed distribution with no outliers.

We have a sample of size ?=20 and x has a Normal distribution.

Answer 1

Solution:

To use t procedures  to make inferences about μ using  , we need population to be Normally distributed or sample size should be large enough so that sampling distribution of sample mean will be approximately Normal, regardless the shape of population distribution.

Option 2 and 4 have Normal distribution , so we can use these samples to use t procedures  to make inferences about μ using  .

Option 3 has sample size n = 60 > 30, hence we can assume large sample size and hence sampling distribution of sample mean will be approximately Normal, regardless the shape of population distribution.Thus we can use this sample to use t procedures  to make inferences about μ using  .

Option 1) has sample size = n= 20 and x has a right‑skewed distribution with an outlier.

Since sample size n is small ( < 30) and  x has a right‑skewed distribution with an outlier, thus we can not use this case to use t procedures  to make inferences about μ using  .

Thus correct answer is first option:

We have a sample of size ?=20 and x has a right‑skewed distribution with an outlier.