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Chapter 8: Q31 (page 373)

Type I and Type II Errors. In Exercises 29鈥�32, provide statements that identify the type I error and the type II error that correspond to the given claim. (Although conclusions are usually expressed in verbal form, the answers here can be expressed with statements that include symbolic expressions such as p = 0.1.).

The proportion of adults who use the internet is greater than 0.87.

Short Answer

Expert verified

A type I error occurs when the actual value of the proportion is equal to 0.87, and the researcher rejects the claim p=0.87and supports the claim that p>0.87.

A type II error occurs when the actual value of the proportion is greater than 0.87,and the researcher fails to reject the claim p=0.87.

Step by step solution

01

Given information

It is claimed that the proportion of adults who use the internet is greater than 0.87.

02

Hypotheses

Let p be the population proportion of adults who use the internet.

According to the stated claim, the following hypotheses are set up:

Null hypothesis, H0:p=0.87.

Alternative hypothesis, HA:p>0.87.

03

Types of errors

The two types of errors made while conducting hypotheses tests are defined below.

Type I error: Rejecting the null hypothesis when the null hypothesis is true is a type I error and is denoted by 伪.

Type II error: Failing to reject the null hypothesis when the null hypothesis is false is a type II error and is denoted by 尾.

In accordance with the given claim, the following statements define the type I error and the type II error:

Type I error: When the actual value of the proportion is equal to 0.87, and the researcher rejects the claim p=0.87and supports the claim p>0.87, a type I error is made.

Type II error: When the actual value of the proportion is greater than 0.87, and the researcher fails to reject the claim p=0.87, a type II error is made.

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Most popular questions from this chapter

In Exercises 9鈥�12, refer to the exercise identified. Make subjective estimates to decide whether results are significantly low or significantly high, then state a conclusion about the original claim. For example, if the claim is that a coin favours heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favours heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).

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Testing Hypotheses. In Exercises 13鈥�24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.

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Type I and Type II Errors. In Exercises 29鈥�32, provide statements that identify the type I error and the type II error that correspond to the given claim. (Although conclusions are usually expressed in verbal form, the answers here can be expressed with statements that include symbolic expressions such as p = 0.1.).

The proportion of people who require no vision correction is less than 0.25.

Testing Hypotheses. In Exercises 13鈥�24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.

Cans of Coke Data Set 26 鈥淐ola Weights and Volumes鈥� in Appendix B includes volumes (ounces) of a sample of cans of regular Coke. The summary statistics are n = 36, x = 12.19 oz, s = 0.11 oz. Use a 0.05 significance level to test the claim that cans of Coke have a mean volume of 12.00 ounces. Does it appear that consumers are being cheated?

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