Question

1. If a sample size grows larger, what is the impact on Type I errors?
2. Why is a Type I error similar to a false alarm?
3. Provide an example of a situation when you want a very small Type I error possibility.
4. Provide an example of a situation when you want a very small Type II error possibility.

Answer 1

1. As we assign our probability of type I errors ourselves for determining the test hence increase in sample size would not effect the probability of type I error .
2. Type I error is called false alarm because we reject the true null,i.e even when our null hypothesis is true we reject that.For example if our null hypothesis is such that our product is good.But for type I error we would think the product is faulty even if it's good .Hence it's a false alarm.
3. If I'm a manufacturer and my null hypothesis is " product is above the quality ".Here type I error is rejection of above quality products .Now if my type I error probability increases ,many of my above quality products would get rejected and I would be in loss.So I would like to have a low type I error in that case.
4. If I'm buying a product the null hypothesis would be " product is above the quality" .And the type II error is acceptance of below quality products.Now if type II error increases ,I would be buying a whole lot of below quality products,which is my loss.So here I want the type II error to be small.