Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Q. T8.4 (page 549)

Many television viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, Timex Group USA wishes to estimate the true proportion p of all consumers who believe what is shown in Timex television commercials. What is the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05or less at a 99%confidence level?

a. 550

b. 600

c. 650

d. 700

e. 750

Short Answer

Expert verified

The required smallest number of consumers is 600

The correct option is(b)

Step by step solution

01

Given information

Confidence level =99%

Margin of error(E)=0.05

02

The objective is to find out the smallest number of consumers to have the margin of error at most 0.05at 99%the confidence level.

We know,

The formula to compute the sample size is:

n=p^(1-p^)zα2E2

There is no information about p^provided here.

Thus, assume is to be 0.50

According to the standard norma table, the value of zα2corresponding to99%the confidence level is 2.576

The sample size is calculated as follows:

n=p^(1-p^)zα2E2=0.50(1-0.50)2.5760.052=664

The smallest number of consumers is 600

Therefore, the correct option is(b)

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

More income The 2015American Community Survey estimated the median household income for each state. According to ACS, the 90%confidence interval for the 2015

median household income in New Jersey is \(72,222±\)610.

a. Interpret the confidence interval.

b. Interpret the confidence level.

High tuition costs Glenn wonders what proportion of the students at his college believe that tuition is too high. He interviews an SRS of 50 of the 2400 students and finds 38 of those interviewed think tuition is too high.

10Bottling cola A particular type of diet cola advertises that each can contains 12 ounces of the beverage. Each hour, a supervisor selects cans at random, measures their contents, and computes a 95%confidence interval for the true mean volume. For one particular hour, the 95%confidence interval is 11.97ounces to 12.05ounces.

a. Does the confidence interval provide convincing evidence that the true mean volume is different than 12ounces? Explain your answer.

b. Does the confidence interval provide convincing evidence that the true mean volume is 12ounces? Explain your answer.

Price cuts (4.2) Stores advertise price reductions to attract customers. What type of price
cut is most attractive? Experiments with more than one factor allow insight into
interactions between the factors. A study of the attractiveness of advertised price discounts
had two factors: percent of all foods on sale (25%, 50%, 75%, or 100%) and whether the discount was stated precisely (e.g., as in “60% off”) or as a range (as in “40% to 70% off”). Subjects rated the attractiveness of the sale on a scale of 1 to 7.
a. List the treatments for this experiment, assuming researchers will use all combinations of the two factors.
b. Describe how you would randomly assign 200 volunteer subjects to treatments.
c. Explain the purpose of the random assignment in part (b).
d. The figure shows the mean ratings for the eight treatments formed from the two factors.35 Based on these results, write a careful description of how percent on sale and precise discount versus range of discounts influence the attractiveness of a sale.

You want to compute a 90%confidence interval for the mean of a population with an unknown population standard deviation. The sample size is 30. What critical value should you use for this interval?

a. 1.645

b. 1.699

c. 1.697

d. 1.96

e. 2.045
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision 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