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Chapter 8: Problem 46

Suppose you are testing someone to see whether he or she can tell butter from margarine when it is spread on toast. You use many bite-sized pieces selected randomly, half from buttered toast and half from toast with margarine. The taster is blindfolded. The null hypothesis is that the taster is just guessing and should get about half right. When you reject the null hypothesis when it is actually true, that is often called the first kind of error. The second kind of error is when the null is false and you fail to reject. Report the first kind of error and the second kind of error.

Short Answer

Expert verified
A Type I error (or the first kind of error) in this experiment would mean that we incorrectly conclude the taster can differentiate between buttered and margarine toast when they actually cannot. A Type II error (or the second kind of error) would mean we incorrectly conclude the taster cannot differentiate between buttered and margarine toast when they actually can.

Step by step solution

01

Understanding Hypothesis Testing

The first step is to understand what hypothesis testing is. This is a statistical method used to make a decision about a population based on sample data. Here, the null hypothesis it that the taster is just guessing and should get about half right.
02

Define First Type of Error (Type I Error)

Next, a type I error, also known as a false positive, occurs when the null hypothesis is true, but is incorrectly rejected. In the context of this experiment, a type I error would mean we mistakenly conclude the taster can differentiate between buttered and margarine toast, when in reality, they are only guessing.
03

Define Second Type of Error (Type II Error)

A type II error, also known as a false negative, takes place when the null hypothesis is false, but is incorrectly failed to be rejected. In the context of this experiment, a type II error would mean we mistakenly conclude the taster cannot differentiate between buttered and margarine toast, when in reality, they can.

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