A What are the fundamental differences between hypothesis te

(A) What are the fundamental differences between hypothesis tests with z scores and t statistics? (B) How is this t statistic is calculated? (C) Explain why one should calculate effect size in addition to simply conducting hypothesis testing.

Solution

a)

We use the z statistic instead of t when we know the population standard deviation and a sufficiently large sample size (usually, n>30). T statistics is used when we have an insufficiently large sample size,a nd we do not know the population standard deviaiton.

b)

t statistic is calculated in a similar way,

t = (X - u) * sqrt(n) / s

where X= sample mean
u = hypothesized mean
n = sample size
s = sample standard deviation

c)

Because the effect size measures the strength of the phenomenon, while hypothesis testing only desires to know if the phenomenon simply happened by chance or not. So, the phenomenon may be significant in terms of probability, but may be not practically signficant. That\'s why we measure the effect size.