Question

We are to test to see if there is evidence of life on Mars by examining soil samples from the red planet for tell-tale signs of life (cigarettes, half-eaten pop tarts, coke bottles, etc.). The null hypothesis is: No Life on Mars. If we conclude on the basis of our data that there is or was Life there, we’d want to be very sure of our result. In this case, we’d set α to be a very very _______ number. While this would have the desired effect, it would have the side effect of making it more likely to make a type II error. What is a Type II error in this context?

	a.	Large AND   Type II: Conclude Life on Mars doesn’t exist -- then you find out it really does exist.
	b.	Large AND   Type II: Conclude Life on Mars exists -- then you find out it doesn’t exist.
	c.	Small AND   Type II: Conclude Life on Mars doesn’t exist -- then you find out it really does exist.
	d.	Small AND   Type II: Conclude Life on Mars exists -- then you find out it doesn’t exist.

Answer 1

The lower the significance level, the stronger the evidence required to reject the null hypothesis.

Here the null hypothesis is that there is or was no life on Mars. Alternate hypothesis is that there is or was life on Mars. Hence, if we keep the significance level small, we can be very sure that we are correct if we choose to reject null hypothesis and accept alternate hypothesis (there is or was life on Mars).

A Type II error is failure to reject false null hypothesis. Here, it means failing to reject that life on Mars doesn't exists when it actually exists. In other words, Conclude Life on Mars doesn’t exist -- then you find out it really does exist.

Hence, Option C is correct.