Why do t distributions tend to be flatter and more spread ou

Why do t distributions tend to be flatter and more spread out than the normal distribution is? The of the t statistic contains the which is for different samples. The z-score uses the ,which is for different samples. Therefore, the t statistic has variability.

Solution

T distribution used sample standard deviation and z-distribution used population standard devaition. Since t-distribution use sample standard deviation, so it is more variable than population standard devaition. As the sample size incraeses it becomes close to normal distrbution.

\"The distribution of t statistics contains the sample standard deviation, which is different for different samples. The z-score uses the population standard devaition, which is same for different samples. Therefore t-statistics has more variability. \"