/*! 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} Q4 Normality Requirement What does ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Q4 (page 327)

Normality Requirement What does it mean when we say that the confidence interval methodsof this section are robust against departures from normality?

Short Answer

Expert verified

The confidence interval method will give correct results even if the sample is not from a population that perfectly follows the normal distribution and the sample size is small. The condition that the distribution is approximately symmetric and bell-shaped should be satisfied.

Step by step solution

01

Given information

A sample of 50 Verizon airport data speeds is considered to estimate the value of the mean Verizon airport data speed.

02

Normality condition of the confidence interval

One of the requirements to construct a confidence interval estimate of the population mean is that either the sample should be from a normally distributed population or the sample size is large.

But this requirement is not very strict and is robust against departures from normality.

This means that if the sample is somewhat bell-shaped, has no outliers, and the sample size is small (between 15 and 30), the confidence interval computed will work well and will be accurate.

Thus, the method of the confidence interval being robust against departures from normality means that a distribution close to the normal distribution will also work if the sample size is small.

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

Critical Thinking. In Exercises 17鈥�28, use the data and confidence level to construct a confidence interval estimate of p, then address the given question.

Medication UsageIn a survey of 3005 adults aged 57 through 85 years, it was found that 81.7% of them used at least one prescription medication (based on data from 鈥淯se of Prescription and Over-the-Counter Medications and Dietary Supplements Among Older Adults in the United States,鈥� by Qato et al.,Journal of the American Medical Association,Vol. 300, No. 24).

a.How many of the 3005 subjects used at least one prescription medication?

b.Construct a 90% confidence interval estimate of thepercentageof adults aged 57 through 85 years who use at least one prescription medication.

c.What do the results tell us about the proportion of college students who use at least one prescription medication?

Confidence Intervals. In Exercises 9鈥�24, construct the confidence interval estimate of the mean.

In a study of speed dating conducted at Columbia University, female subjects were asked to rate the attractiveness of their male dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive). Use a 99% confidence level. Can the result be used to estimate the mean amount of attractiveness of the population of all adult males?

5 8 3 8 6 10 3 7 9 8 5 5 6 8 8 7 3 5 5 6 8 7 8 8 8 7

Coping with No Success: According to the Rule of Three, when we have a sample size n with x = 0 successes, we have 95% confidence that the true population proportion has an upper bound of 3/n. (See 鈥淎 Look at the Rule of Three,鈥� by Jovanovic and Levy, American Statistician, Vol. 51, No. 2.)a. If n independent trials result in no successes, why can鈥檛 we find confidence interval limits by using the methods described in this section? b. If 40 couples use a method of gender selection and each couple has a baby girl, what is the 95% upper bound for p, the proportion of all babies who are boys?

Sample Size. In Exercises 29鈥�36, find the sample size required to estimate the population mean.

Mean Weight of Male Statistics Students Data Set 1 鈥淏ody Data鈥� in Appendix B includes weights of 153 randomly selected adult males, and those weights have a standard deviation of 17.65 kg. Because it is reasonable to assume that weights of male statistics students have less variation than weights of the population of adult males, let 蟽=17.65鈥�kg. How many male statistics students must be weighed in order to estimate the mean weight of all male statistics students? Assume that we want 90% confidence that the sample mean is within 1.5 kg of the population mean. Does it seem reasonable to assume that weights of male statistics students have less variation than weights of the population of adult males?

Years in college Listed below are the numbers of years it took for a random sample of college students to earn bachelor鈥檚 degrees (based on the data from the National Center for Education Statistics). Construct a 95% confidence interval estimate of the mean time for all college students to earn bachelor鈥檚 degrees. Does it appear that college students typically earn bachelor鈥檚 degrees in four years? Is there anything about the data that would suggest that the confidence interval might not be good result?

4 4 4 4 4 4 4.5 4.5 4.5 4.5 4.5 4.5

6 6 8 9 9 13 13 15
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

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.