Question

Type I Error and Type II Error

a. In general, what is a type I error? In general, what is a type II error?

b. For the hypothesis test in Exercise 6 “BMI for Miss America,” write a statement that would be a type I error, and write another statement that would be a type II error.

Short answer

a.In general, the type I error is the probability of rejecting a null hypothesis when it is correct. Type II error is the probability offailing to reject a null hypothesis when it is wrong.

b. Type I error concludes that the BMI is less than 20.16 when actually it is equal to 20.16. Type II error concludes that the BMI is equal to 20.16 when actually it is less than 20.16.

Step-by-step solution

Describe the types of errors

a.

In testing of hypothesis, there are two types of decisions toward the null hypothesis; reject or fail to reject the null hypothesisafter inspecting sample from the whole population.

In this process, there is a risk of making the wrong decision and these wrong decisions are of two types, Type I error and Type II error.

Define Type I and Type II error

The error that occurs due to the rejection of a null hypothesis when it is true is called a Type I error.

Similarly, the error that occurs due to the failure to reject a null hypothesis when it is actually false is known as a Type II error.

Identify the Type I error and Type II error for Exercise 6

b.

Refer to Exercise 6 for the claim that the BMI for recent winners is significantly smaller than those from the 1920s and 1930s, which is 2016.

Thus, the hypotheses are as follows:

$$\begin{gathered} H_o:\mu =20.16 \\ {H}_1:\mu <20.16 \end{gathered}$$

In this case, Type I error would be committed if the null hypothesis is rejected by mistake. This implies, the population mean BMI was actually 20.16, but it is concluded that the BMI is lesser than 201.6.

Similarly, suppose the mean BMI is less than 20.16, and the decision-maker decides that the mean BMI is equal to 20.16, then it will be a Type II error.