Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 9: Q 86. (page 608)

Upscale restaurant You are thinking about opening a restaurant and are searching for a good location. From the research you have done, you know that the mean income of those living near the restaurant must be over \(85,000to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50people living near one potential site. Based on the mean income of this sample, you will perform a test at the

α=0.05 significance level of H0:μ=\)85,000versus Ha:μ>\(85,000, where μ is the true mean income in the population of people who live near the restaurant. The power of the test to detect that μ=\)86,000is 0.64 Interpret this value.

Short Answer

Expert verified

There is 64 percent probability that finds the convincing proof to help the alternative hypothesisμ>$85000

Step by step solution

01

Given information

H0:μ=$85000H1:μ>$85000μA=alternativemean=$86000

α=significancelevel=0.05

Power =0.64=64%

02

Concept

When the alternative hypothesis is true, the power is the probability of rejecting the null hypothesis.

03

Explanation

If the genuine mean income in the population of persons who live near the restaurant is $86000 there is a 64 percent chance that the alternative hypothesis μ>$85000 will be supported.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Bags of a certain brand of tortilla chips claim to have a net weight of 14ounces. Net weights vary slightly from bag to bag and are Normally distributed with mean μ . A representative of a consumer advocacy group wishes to see if there is convincing evidence that the mean net weight is less than advertised and so intends to test the hypotheses

H0:μ=14Ha:μ<14

A Type I error in this situation would mean concluding that the bags

a. are being underfilled when they aren’t.

b. are being underfilled when they are.

c. are not being underfilled when they are.

d. are not being underfilled when they aren’t.

e. are being overfilled when they are underfilled

Attitudes The Survey of Study Habits and Attitudes (SSHA) is a

psychological test with scores that range from 0to200.. The mean score for U.S. college students is115. A teacher suspects that older students have better attitudes toward school. She gives the SSHA to an SRS of 45students from the more than 1000students at her college who are at least 30years of age. The teacher wants to perform a test at the α=0.05significance level of

H0:μ=115Ha:μ>115

where μ=the mean SSHA score in the population of students at her college who are at least 30years old. Check if the conditions for performing the test are met.

pg559¯

No homework Refer to Exercises 1 and 9. What conclusion would you make at theα=0.05α=0.05level?

Clean water The Environmental Protection Agency (EPA) has determined that safe

drinking water should contain at most 1.3mg/liter of copper, on average. A water supply company is testing water from a new source and collects water in small bottles at each of30randomly selected locations. The company performs a test at the α=0.05 significance level ofH0:μ=1.3versus Ha:μ>1.3, where μ is the

true mean copper content of the water from the new source.

a. Describe a Type I error and a Type II error in this setting.

b. Which type of error is more serious in this case? Justify your answer.

c. Based on your answer to part (b), do you agree with the company’s choice of α=0.05? Why or why not?

Stating hypotheses

a. A change is made that should improve student satisfaction with the parking situation at your school. Before the change, 37%of students approve of the parking that's provided. The null hypothesis H0:p∧=0.37H0:p^=0.37is tested against the alternative Ha: p∧>0.37Ha:p^>0.37

b. A researcher suspects that the mean birth weights of babies whose mothers did not see a doctor before delivery is less than 3000 grams. The researcher states the hypotheses as

H0:μ=3000gramsH0:μ=3000grams

Ha:μ≤2999gramsHa:μ≤2999grams
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free