/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 56. Losing weight A Gallup poll foun... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Q. 56. (page 583)

Losing weight A Gallup poll found that 59% of the people in its sample said 鈥淵es鈥� when asked, 鈥淲ould you like to lose weight?鈥� Gallup announced: 鈥淔or results based on the total sample of national adults, one can say with 95% confidence that the margin of (sampling) error is 卤3 卤3percentage points.鈥�12 Based on the confidence interval, is there convincing evidence that the true proportion of U.S. adults who would say they want to lose weight differs from 0.55? Explain your reasoning

Short Answer

Expert verified

The required answer is :

Yes, there are sufficient evidence

Step by step solution

01

Given information

Sample proportion (p^)=59%=0.59

Margin of error(E)=卤3%=卤0.03

02

The objective is to find out the confidence interval 

The formula for calculating the confidence interval for a population proportion is as follows:

Confidence interval =p^卤E

The 95%confidence interval can be calculated as follows:

Confidence interval :

=p^卤E=0.59卤0.03=(0.56,0.62)

Therefore, the confidence interval is(0.56,0.62)

03

The objective is to find whether there are sufficient evidence to conclude that the proportion of U.S adults who are saying that they are interesting in losing the weight is different from 0.55 . 

Because 0.55does not fall within the above-mentioned confidence interval. Thus, there is sufficient evidence to conclude that the proportion of US adults who say they want to lose weight is greater than 0.55

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

Better parking A local high school makes a change that should improve student

satisfaction with the parking situation. Before the change, 37%of the school鈥檚 students approved of the parking that was provided. After the change, the principal surveys an SRS of 200from the more than 2500students at the school. In all, 83students say that they approve of the new parking arrangement. The principal cites this as evidence that the change was effective.

a. Describe a Type I error and a Type II error in this setting, and give a possible

consequence of each.

b. Is there convincing evidence that the principal鈥檚 claim is true?

According to the Bureau of Labor Statistics, the average age of American workers is 41.9years. The manager of a large technology company believes that the company鈥檚 employees tend to be younger, on average. So she takes a random sample of 12 employees and records their ages.

Here are the data:

27 38 32 24 30 47 42 38 27 43 37 33

a. State appropriate hypotheses for testing the manager鈥檚 belief. Be sure to define the parameter of interest.

b. State the conditions for performing a test of the hypotheses in (a), and determine whether each condition is met.

c. The P-value of the test is0.003. Interpret this value. What conclusion would you make?

Ski jump When ski jumpers take off, the distance they fly varies considerably depending on their speed, skill, and wind conditions. Event organizers must position the landing area to allow for differences in the distances that the athletes fly. For a particular competition, the organizers estimate that the variation in distance flown by the athletes will be \(\sigma=10\) \(\sigma=10\) meters. An experienced jumper thinks that the organizers are underestimating the variation.

Better parking A local high school makes a change that should improve student satisfaction with the parking situation. Before the change, 37% of the school鈥檚 students approved of the parking that was provided. After the change, the principal surveys an SRS of students at the school. She would like to perform a test of H0:p=0.37Ha:p>0.37where p is the true proportion of students at school who are satisfied with the parking

situation after the change.

a. The power of the test to detect that p=0.45 based on a random sample of 200 students and a significance level of 伪=0.05 is 0.75 Interpret this value.

b. Find the probability of a Type I error and the probability of a Type II error for the test in part (a).

c. Describe two ways to increase the power of the test in part (a).

A95%confidence interval for the proportion of viewers of a certain reality television

show who are over 30 years old is (0.26,0.35). Suppose the show's producers want to est the hypothesis \H0:p=0.25against Ha: Ha:p鈮�0.25. Which of the following is an appropriate conclusion for them to draw at the 伪=0.05

a. Fail to reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old equals 0.25

b. Fail to reject H0there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from0.25.

c. Reject H0; there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from 0.25

. d. Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old is greater than 0.25.

e. Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from0.25.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Discrete 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.