Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Q5 (page 339)

In Exercises 5–8, use the given information to find the number of degrees of freedom, the critical values X2 L and X2R, and the confidence interval estimate of σ. The samples are from Appendix B and it is reasonable to assume that a simple random sample has been selected from a population with a normal distribution.

Nicotine in Menthol Cigarettes 95% confidence;n= 25,s= 0.24 mg.

Short Answer

Expert verified

The degrees of freedom is 24.

The critical values are χL2=12.401 and χR2=39.364.

The 95% confidence interval estimate of is 0.19mg<σ<0.33mg.

Step by step solution

01

Given information

The size of the sample is n=25.

The sample standard deviation is s=0.24.

The level of confidence is 95%.

02

Compute the degrees of freedom, critical values and confidence interval estimate of σ

The degrees of freedom (df) is computed as,

df=n-1=25-1=24

Using the Chi-square table, the critical values are χL2=12.401and χR2=39.364.

The 95% confidence interval estimate of is computed as,

role="math" localid="1648052944759" n-1s2χR2<σ<n-1s2χL225-10.24239.364<σ<25-10.24212.4010.19<σ<0.33

Therefore, the 95% confidence interval estimate of role="math" localid="1648052981275" σisrole="math" localid="1648052969717" 0.19mg<σ<0.33mg.

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

Cell Phone Radiation Here is a sample of measured radiation emissions (cW/kg) for cell phones (based on data from the Environmental Working Group): 38, 55, 86, 145. Here are ten bootstrap samples: {38, 145, 55, 86}, {86, 38, 145, 145}, {145, 86, 55, 55}, {55, 55, 55, 145}, {86, 86, 55, 55}, {38, 38, 86, 86}, {145, 38, 86, 55}, {55, 86, 86, 86}, {145, 86, 55, 86}, {38, 145, 86, 556}.

a. Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the population mean.

b. Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the population standard deviation.

How Many? The examples in this section all involved no more than 20 bootstrap samples. How many should be used in real applications?

Determining Sample Size. In Exercises 31–38, use the given data to find the minimum sample size required to estimate a population proportion or percentage.

Airline Seating

You are the operations manager for American Airlines, and you are considering a higher fare level for passengers in aisle seats. You want to estimate the percentage of passengers who now prefer aisle seats. How many randomly selected air passengers must you survey? Assume that you want to be 95% confident that the sample percentage is within 2.5 percentage points of the true population percentage.

a. Assume that nothing is known about the percentage of passengers who prefer aisle seats.

b. Assume that a prior survey suggests that about 38% of air passengers prefer an aisle seat

(based on a 3M Privacy Filters survey).

In Exercises 9–16, assume that each sample is a simple

random sample obtained from a population with a normal distribution.

Comparing Waiting Lines

a. The values listed below are waiting times (in minutes) of customers at the Jefferson Valley Bank, where customers enter a single waiting line that feeds three teller windows. Construct a95% confidence interval for the population standard deviation .

6.5 6.6 6.7 6.8 7.1 7.3 7.4 7.7 7.7 7.7

b. The values listed below are waiting times (in minutes) of customers at the Bank of Providence, where customers may enter any one of three different lines that have formed at three teller windows. Construct a 95% confidence interval for the population standard deviation .

4.2 5.4 5.8 6.2 6.7 7.7 7.7 8.5 9.3 10.0

c. Interpret the results found in parts (a) and (b). Do the confidence intervals suggest a difference in the variation among waiting times? Which arrangement seems better: the single-line system or the multiple-line system?

Using Correct Distribution. In Exercises 5–8, assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) Find the critical value tα2,(b) find the critical value ,or zα2(c) state that neither the normal distribution nor the t distribution applies.

Denver Bronco Salaries confidence level is 99%,σ=3342thousand dollars, and the histogram of 61 player salaries (thousands of dollars) is shown in Exercise 6.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

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