Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Q 66. (page 542)

Check them all Determine if the conditions are met for constructing a confidence interval for the population mean in each of the following settings.

a. We want to estimate the average age at which U.S. presidents have died. So we obtain a list of all U.S. presidents who have died and their ages at death.

b. Do teens text more than they call? To find out, an AP Statistics class at a large high school collected data on the number of text messages and calls sent or received by each of 25randomly selected students. The boxplot displays the difference (Texts − Calls) for each student.

Short Answer

Expert verified

a. The conditions not met are: Random Sample and Independent.

b. Condition not met is of Large Sample.

Step by step solution

01

Part (a) Step 1: Given Information

It is given that population is taken of all US president.

02

Part (a) Step 2: Explanation

Conditions are:

  • Random: In sample, all US president are included. It cannot be random sample.
  • Independence: Sample of US presidents can never be less than 10%of total population of US president.
  • Large Sample Size: It will be >30as they are for sure more than 30

The conditions not met are: Random Sample and Independent.

03

Part (b) Step 1: Given Information

It is given that n=25

Population is of all the students.

04

Part (b) Step 2: Explanation

Conditions are:

  • Random: This is satisfied as students are selected randomly.
  • Independent: 25<10%of population of all students.
  • Large Sample Size: 25<30. This is not met.

Condition of Large Sample is not met.

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

Willows in Yellowstone Writers in some fields summarize data by giving x ̄ and its

standard error rather than x¯andSX.Biologists studying willow plants in Yellowstone National Park reported their results in a table with columns labeled x¯andSX The table entry for the heights of willow plants (in centimeters) in one region of the park was 61.55±19.03. The researchers measured a total of 23plants.

a. Find the sample standard deviation sxfor these measurements.

b. A hasty reader believes that the interval given in the table is a 95% confidence interval for the mean height of willow plants in this region of the park. Find the actual confidence level for the given interval.

Fun size candyA candy bar manufacturer sells a “fun size” version that is advertised to weigh 17grams. A hungry teacher selected a random sample of 44fun size bars and found a 95%confidence interval for the true mean weight to be 16.945grams to 17.395grams.

a. Does the confidence interval provide convincing evidence that the true mean weight is different than 17grams? Explain your answer.

b. Does the confidence interval provide convincing evidence that the true mean weight is 17grams? Explain your answer.

The Large Counts condition When constructing a confidence interval for a population proportion, we check that both np∧andn1-p∧are at least 10

a. Why is it necessary to check this condition?

b. What happens to the capture rate if this condition is violated?

A 90%confidence interval for the mean μ of a population is computed from a random sample and is found to be90±30. Which of the following could be the 95%confidence interval based on the same data?

a. 90±21

b. 90±30

c. 90±39

d. 90±70

e. Without knowing the sample size, any of the above answers could be the 95%confidence interval.

You have measured the systolic blood pressure of an SRS of 25company employees. A 95%confidence interval for the mean systolic blood pressure for the employees of this company is (122,138). Which of the following statements is true?

a. 95%of the sample of employees have a systolic blood pressure between 122 and 138.

b. 95%of the population of employees have a systolic blood pressure between 122and138.

c. If the procedure were repeated many times, 95%of the resulting confidence intervals would contain the population mean systolic blood pressure.

d. If the procedure were repeated many times, 95%of the time the population mean systolic blood pressure would be between 122and 138.

e. If the procedure were repeated many times, 95%of the time the sample mean systolic blood pressure would be between 122and138.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

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