STATISTICAL TECHNIQUES AND TOOLS
T DISTRIBUTION
|
Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
|
|
|
Its more accurate for smaller sample sizes
|
|
|
Its more accurate for larger sample sizes
|
|
|
They are the same
|
|
|
None of these.
|
Detailed explanation-1: -Student t-distribution handles estimated standard deviation better because using it with normal distribution (which should have only population standard deviation) will create extra errors (you will incorrectly estimate your type I (and Ii) errors).
Detailed explanation-2: -The reason t-distribution is used in inference instead of normal is due to the fact that the theoretical distribution of some estimators is normal (Gaussian) only when the standard deviation is known, and when it is unknown the theoretical distribution is Student t.
Detailed explanation-3: -The t-distribution limit at infinity degrees of freedom is the normal distribution. In the past, people used tables to calculate the cumulative probability. For the t-table you need to have a separate set of data for any DF value, hence the Z-Table is more detailed and more accurate than the t-table.