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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.

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