Using the T-distribution or normal distribution?

[Johnfeb94]

So, my class got our midterm back and i'm confused on the answer to this question.

Suppose you are given a random sample of 41 observations on student heights in inches and youcalculate a mean of 65” with a standard deviation of 3.75”. You are asked to construct a 95%confidence interval based on this data. Which distribution would you use to find your critical values?
a. the standard normal
b. the standard normal with 41 degrees of freedom
c. the t-distribution with 41 degrees of freedom
d. the t-distribution with 40 degrees of freedom
e. the t-distribution with 39 degrees of freedom

-According to my professor, the answer is D. But I thought you use the t-distribution when the standard deviation is not known and the sample size is 30 or below. What do you think?

Thank you!

 

[Ishuda]

So, my class got our midterm back and i'm confused on the answer to this question.

Suppose you are given a random sample of 41 observations on student heights in inches and youcalculate a mean of 65” with a standard deviation of 3.75”. You are asked to construct a 95%confidence interval based on this data. Which distribution would you use to find your critical values?
a. the standard normal
b. the standard normal with 41 degrees of freedom
c. the t-distribution with 41 degrees of freedom
d. the t-distribution with 40 degrees of freedom
e. the t-distribution with 39 degrees of freedom

-According to my professor, the answer is D. But I thought you use the t-distribution when the standard deviation is not known and the sample size is 30 or below. What do you think?

Thank you!

It might have been better to say "sample variance of 14.0625" or "sample standard deviation of 3.75" as the Students t uses the sample standard deviation (as I understand it) and, IMO, that is what was actually meant. The Students t can be used for degrees of freedom much larger than 30. In fact there are tables available for 250 degrees of freedom, i.e
http://albertskblog.blogspot.com/2010/08/student-t-distribution-table.html