A random sample of size 39 is taken from a population of 200 members. The sample mean is 66 and the population standard deviation is 11. Construct a % 96 confidence interval to estimate the population mean. What is the point estimate of the population mean?

Hi I have also one question which is going to be really helpful for me to understand this sort of question more logically and comprehensively.

While we are working on the T Value, I have experienced that we are finding t value with two different ways;

1) Regardless of the n value ( number of sample) we only focus on confidence interval if that is % 95 we put 1.960 or % 90 1.645.

2) Sometimes we also calculate the d value with df and confidence interval.

I can not distinguish these two types while working on the question. May I get clarification for these detail mentioned above and step by step solution for the question on the top of the page.

Thank you