/*! 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 17. Explaining confidence A 95%聽con... [FREE SOLUTION] | 91影视

91影视

Explaining confidence A 95%confidence interval for the mean body mass index (BMI) of young American women is 26.80.6. Discuss whether each of the following explanations is correct, based on that information.

a. We are confident that 95%of all young women have BMI between 26.2and 27.4.

b. We are 95%confident that future samples of young women will have mean BMI

between 26.2and27.4.

c. Any value from 26.2to27.4is believable as the true mean BMI of young American women.

d. If we take many samples, the population mean BMI will be between 26.2and 27.4in about 95%of those samples.

e. The mean BMI of young American women cannot be 28.

Short Answer

Expert verified

a. Statement a is incorrect.

b. Statement b is incorrect.

c. Statement c is correct.

d. Statement d is incorrect.

e. Statement e is incorrect.

Step by step solution

01

Given Information

It is given that 95%confidence interval for mean body index is(26.2,27.4)

02

To Explain statement a is correct or not on the basis of given information.

From given data, it is incorrect because confidence interval is about BMI of young women, not about BMI of individual women.

03

To Explain statement b is correct or not on the basis of given information.

The statement is incorrect because it is not confirmed that true population mean is between 26.2and27.4.

The mean may or may not lie in confidence interval for further samples.

The statement is incorrect.

04

To Explain statement c is correct or not on the basis of given information.

The statement is correct because there is 95%confidence that population mean lie between 26.2and27.4.

The exact value is not known, so it can be any value between 26.2and27.4

The statement is correct.

05

To Explain statement d is correct or not on the basis of given information.

There will be no change in population mean. I will be value between 26.2and27.4.

That is, 100%or 0%of time.

So, the statement is incorrect.

06

To Explain statement e is correct or not on the basis of given information. 

It is incorrect as there are 95%of samples has 95%confidence interval having true population mean.

So,(26.2,27.4)may be among remaining5%samples not having true population mean.

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

Scientists collect data on the blood cholesterol levels (milligrams per deciliter of blood) of a random sample of 24laboratory rats. A 95%confidence interval for the mean blood cholesterol level is 80.2to 89.8. Which of the following would cause the most worry about the validity of this interval?

a. There is a clear outlier in the data.

b. A stem plot of the data shows a mild right skew.

c. You do not know the population standard deviation .

d. The population distribution is not exactly Normal.

e. None of these are a problem when using a t interval.

More weight loss Refer to Exercise 6. Interpret the confidence level.

Student body totals Use your interval from Exercise 40 to construct and interpret a 99%confidence interval for the total number of students at the school that the student body president can identify by name. Then use your interval to evaluate the president鈥檚 claim.

Election polling Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. We want to estimate the proportion p of all registered voters in the city who plan to vote for Chavez with 95%confidence and a margin of error no greater than 0.03. How large a random sample do we need?

Prayer in school A New York Times/CBS News Poll asked a random sample of U.S. adults the question 鈥淒o you favor an amendment to the Constitution that would permit organized prayer in public schools?鈥 Based on this poll, the 95%confidence interval for the population proportion who favor such an amendment is (0.63,0.69).

a. Interpret the confidence interval.

b. What is the point estimate that was used to create the interval? What is the margin of error?

c. Based on this poll, a reporter claims that more than two-thirds of U.S. adults favor such an amendment. Use the confidence interval to evaluate this claim.

See all solutions

Recommended explanations on Math Textbooks

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.