Question

A border protection avatar. The National Center for Border Security and Protection has developed the "Embodied Avatar"—a kiosk with a computer-animated border guard that uses artificial intelligence to scan passports, check fingerprints, read eye pupils, and asks questions of travellers crossing the U.S. border. (National Defense Magazine, February 2014.) Based on field tests, the avatar's developer claims that the avatar can detect deceitful speech correctly 75% of the time.

a. Identify the parameter of interest.

b. Give the null and alternative hypotheses for testing the claim made by the avatar's developer.

c. Describe a Type I error in the words of the problem.

d. Describe a Type II error in the words of the problem

Short answer

a.In the study, the parameter of interest is the population proportion of deceitful speech recognized by the avatar.

b. The null hypothesis is H₀ = p = 0.75, and the alternative hypothesis is H_a: p ≠ 0.75.

c.The conclusion is that the population proportion of deceitful speech recognized by the avatar differs from 75%, but it is 75%

d. The conclusion is that the population proportion of deceitful speech recognized by the avatar does not differ from 75%, but it differs from 75%

Step-by-step solution

Given information

According to the avatar's developer, deceptive speech can be accurately detected 75% of the time.

Identifying the parameter of interest

a.

In the study, the parameter of interest is the population proportion of deceitful speech recognized by the avatar, denoted as p.

Setting up the hypotheses

b.

Null hypothesis:

H₀ = p = 0.75

That is, the population proportion of deceitful speech recognized by the avatar is 0.75.

Alternative hypothesis:

H_a: p ≠ 0.75

That is, the population proportion of deceitful speech recognized by the avatar differs from 0.75.

Describing the type I error

c.

Type I error is the error committed to rejecting a null hypothesis when it is true. The conclusion is that the population proportion of deceitful speech recognized by the avatar differs from 75%. Still, in reality, the population proportion of deceitful speech recognized by the avatar does not vary from 75%.

Describing the type II error

d.

Type II error is the error committed to accepting a null hypothesis when it is false. The conclusion is that the population proportion of deceitful speech recognized by the avatar does not differ from 75%. Still, in reality, the population proportion of deceitful speech recognized by the avatar differs from 75%.