Question

Bill and Sarah both have single sample data--Bill has n=4 measurements in his data set, and Sarah has n=28 in hers. Both mistakenly conduct single sample t-tests rather than z-tests. For whom is this situation more problematic (ie: for whom will the results be less accurate), and why? Describe in terms of the z and t distributions

Answer 1

In terms of Z score both shoudl be accurate as standard error can be taken care by the no. of the sample size.

However, in terms of t test, one need to idetify the degree of freedom and based ont this, critical t value can be caluculated

As no. of the sample size increased, t distribution converges to the z distribution.

So in terms of sample size, n=28 would have more identical z distiribuuiton if we measure the t distribuiton.

based on this,sarah has more accurate result than the bill has.

So for Bill has the situtaion more probalemtic than Sarah.

As if we take n =25-30, t distribution and z distribuiton are same.