Question

Topic: What can you say about a sample mean or a sample proportion being about 2 SEs away from the population mean or the true proportion? What can you NOT say?

Discuss (4-5 sentences minimum) these questions.  

Answer 1

Ans. When we have a normal model for the sampling distribution, 95% of the sample proportions fall within 2 standard errors of the population proportion.

Similarly the percentage of the sample proportions decreases when the standard error distance decreases and the percentage increases when the standard error distance increases.

So when 99% of the sample proportions fall within a certain standard error distance of the population proportion, that standard error distance is going to be greater than 2 standard errors.