/*! 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} Q. 6.14 According to the Census Bureau, ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q. 6.14 (page 437)

According to the Census Bureau, 13%of American adults (aged 18 and over) are Hispanic. An opinion poll plans to contact an SRS of 1200adults.

a. What is the mean number of Hispanics in such samples? What is the standard deviation?

b. Should we be suspicious if the sample selected for the opinion poll contains 10%or less Hispanic people? Calculate an appropriate probability to support your answer.

Short Answer

Expert verified
  1. The obtained values are 渭=156and 蟽=11.6499.
  2. Regardless of the fact that this likelihood is less than 0.05or5%, 180 Hispanics are unlikely to appear by chance, and hence suspicion should be raised.

Step by step solution

01

Part (a) Step 1: Given information

Given:

p=13%=0.13n=1200

Formula used:

渭=np蟽=np(1-p)

02

Part (a) Step 2: Calculation

The average is

渭=np=1200(0.13)=156

A binomial random variable's standard deviation is

蟽=np(1-p)=1200(0.13)(1-0.13)=11.6499
03

Part (b) Step 1: Given information

Given:

15% of the sample contains Hispanic.

p=13%=0.13

Formula used:

P(X=k)=Ckn脳pk脳(1-p)n-k
04

Part(b) Step 2: Calculation

Because the likelihood of the number of successes in the sample is important, the distribution is binomial.

P(X=k)=Ckn脳pk脳(1-p)n-k

Determine if you should be suspicious or not by calculating the likelihood of receiving anything.

1200脳15%=180Hispanics or more extreme:

P(X鈮�180)=鈭�k=1801200C1200n脳0.13k脳(1-0.13)1200-k=0.0235

Despite the fact that this likelihood is less than 0.05 or 5%, 180 Hispanics are unlikely to appear by chance, and hence suspicion should be raised.

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

XA glass act In a process for manufacturing glassware, glass stems are sealed by heating them in a flame. Let X be the temperature (in degrees Celsius) for a randomly chosen glass. The mean and standard deviation of X are 渭X=550掳Cand 蟽X=5.7掳C.

a. Is tempe谐ature a discrete 芯谐 continuous 谐andom variable? Explain 褍芯u谐 answer.

b. The target temperature is 550掳C. What are the mean and standard deviation of the number of degrees off target, D=X-550?

c. A manager asks for results in degrees Fahrenheit. The conversion of X into degrees Fahrenheit is given by Y=95X+32Y=95X+32. What are the mean 渭Yand the standard deviation 蟽Yof the temperature of the flame in the Fahrenheit scale?

Taking the train Refer to Exercise 80 . Use the binomial probability formula to find P(Y=4). Interpret this value.

Spoofing (4.2) To collect information such as passwords, online criminals use "spoofing" to direct Internet users to fraudulent websites. In one study of Internet fraud, students were warned about spoofing and then asked to log into their university account starting from the university's home page. In some cases, the log-in link led to the genuine dialog box. In others, the box looked genuine but, in fact, was linked to a different site that recorded the ID and password the student entered. The box that appeared for each student was determined at random. An alert student could detect the fraud by looking at the true Internet address displayed in the browser status bar, but most just entered their ID and password.

a. Is this an observational study or an experiment? Justify your answer.

b. What are the explanatory and response variables? Identify each variable as categorical or quantitative.

Bag check Thousands of travelers pass through the airport in Guadalajara,

Mexico, each day. Before leaving the airport, each passenger must go through the customs inspection area. Customs agents want to be sure that passengers do not bring illegal items into the country. But they do not have time to search every traveler's luggage. Instead, they require each person to press a button. Either a red or a green bulb lights up. If the red light flashes, the passenger will be searched by customs agents. A green light means "go ahead." Customs agents claim that the light has probability 0.30of showing red on any push of the button. Assume for now that this claim is true. Suppose we watch 20 passengers press the button. Let R=the number who get a red light. Here is a histogram of the probability distribution of R:

a. What probability distribution does R have? Justify your answer.

b. Describe the shape of the probability distribution.

Easy-start mower Refer to Exercise 92 .

a. Calculate and interpret the mean of T.

b. Calculate and interpret the standard deviation of T.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

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.