statistics hypothesis#3

Question

Assume that each of the following conclusions represents an error in hypothesis testing. Indicate whether each of the statements is a Type I or II error.
a) Based on the data, the null hypothesis was rejected.
b) There was no significant difference in quality of work between nurses who work 8- and 12-hours shifts.
c) There was a significant difference between right- and left-handers in their ability to perform a spatial task.
d) The researcher failed to reject the null hypothesis based on these data.

Answer 1

A type I error occurs when the null hypothesis is true but you reject it. A type II error occurs when the null hypothesis is not true but you accept it as true. Note, when you make these errors you don't really know you've made the error until later testing shows your conclusion seems to be wrong.

 

Type I and II errors occur due to statistical anomalies. Let's says you are testing the means of two populations and in fact the means are the same but due to sampling anomaly you happen to draw samples that just happen to be way out in the tail. So, you decide the means are different even though they are the same. Type I error.

 

So, looking at the tests:

 

a) The null hypothesis is rejected meaning that you thought the means were different when in fact they are the same. Type I error.

b) The null hypothesis is accepted (usually null H is that the two values are the same) but they are really not the same.... Type II error.

c) You observe that there is a significant difference between left and right handers when in fact there is none. H₀ would be that they are the same. So, Type I error.

d) H₀ would say they are the same.  You should have rejected the null hypothesis but you didn't. Whatever you are measuring is indeed different but you said they were the same. Type II error.

 

I hope this helps.