Question

Under which circumstances a z-interval should be constructed.

Under which circumstances a t-interval should be constructed.

When can neither a z-interval nor a t-interval be constructed?

Answer 1

Under which circumstances a z-interval should be constructed.

When we are given the value for the population standard deviation and the random sample is come from normally distributed population, then we use the z-interval. Also, if the sample size is very large, then we use the z-interval.

Under which circumstances a t-interval should be constructed.

When we are not given the value for the population standard deviation and the random sample is come from normally distributed population, then we use the t-interval. Also, if the sample size is small, then we use the t-interval.

When can neither a z-interval nor a t-interval be constructed?

When the assumption of the normality is violated, that is, if the random sample is not come from the normally distributed population, then we can neither use a z-interval nor a t-interval.