Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Q 34. (page 522)

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?

Short Answer

Expert verified

a. The sample distribution is approximately normal.

b. The chances are less to catch correct population parameter.

Step by step solution

01

Given Information

We check np^andn(1-p^)≥10during construction of confidence interval for population proportion.

02

Necessity of Conditions

Large Count condition, np^andn(1-p^)should be at least 10. We require large count condition to be satisfied, so that sampling distribution is normal approximately.

If it is not met, sampling distribution of proportion is skewed. Hence, we can't use normal distribution for estimation of confidence interval.

03

If the above Condition is Violated

If the condition is not satisfied, sampling distribution of sample proportion is skewed, hence normal distribution is not used to estimate confidence interval.

Correct population parameter won't be captured.

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

America’s favorite cookie Ann and Tori wanted to estimate the average weight of an Oreo cookie to determine if it was less than advertised (34 grams for 3 cookies). They selected a random sample of 36cookies and found the weight of each cookie (in grams). The mean weight was x̄=11.3921grams with a standard deviation of sX=0.0817grams. Construct and interpret a 90%confidence interval for the true mean weight of an Oreo cookie.

Age and September 11 Refer to Exercise 42. The study also reported that 86% of

millennials included 9/11 in their top-10 list and 70% of baby boomers included 9/11.

a. Explain why you do not have enough information to give confidence intervals for

millennials and baby boomers separately.

b. Do you think a 95%confidence interval for baby boomers would have a larger or smaller margin of error than the estimate from Exercise 42? Explain your answer.

Estimating BMI The body mass index (BMI) of all American young

women is believed to follow a Normal distribution with a standard deviation of about 7.5. How large a sample would be needed to estimate the mean BMI μ in this population to within ±1 with 99% confidence?

Prayer in school Refer to Exercise 5.

a. Explain what would happen to the length of the interval if the confidence level were increased to 99%.

b. How would a 95%confidence interval based on double the sample size compare to the original 95%interval?

c. The news article goes on to say: “The theoretical errors do not take into account

additional errors resulting from the various practical difficulties in taking any survey of public opinion.” List some of the “practical difficulties” that may cause errors which are not included in the ±3 percentage point margin of error.

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.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Mechanics 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