In what situation it is better to use the t-distribution than the normal distribution?
You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.
Which of the following is a difference between the t-distribution and the standard normal Z-distribution group of answer choices?
The correct answer is: (d) The t-distribution has a larger variance than the standard normal distribution.
When to use t-distribution instead of normal distribution?
Depends on your application it can be significantly higher. So we use t-distribution over normal distribution when the sample size is small because the answers are more accurate. T-distribution is generally used for smaller sample sizes so yes to answer your question, its a good practice.
How is the t distribution used to make inferences?
The way the t-distribution is used to make inferences about populations from samples is the model for many of the inferences that statisticians make. Since you will be learning to make inferences like a statistician, try to understand the general model of inference making as well as the specific cases presented.
When to use t distribution in estimating standard error?
When estimating the mean and standard error from a small sample, the t distribution is a more accurate tool than the normal model. This is true for both small and large samples. Use the t distribution for inference of the sample mean when observations are independent and nearly normal.
When is the sampling distribution of the mean nearly normal?
The sampling distribution of the mean is nearly normal when the sample observations are independent and come from a nearly normal distribution. This is true for any sample size. While this seems like a very helpful special case, there is one small problem. It is inherently difficult to verify normality in small data sets.