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Chapter 12: Q. 4 (page 799)

The school board in a certain school district obtained a random sample of 200residents and asked if they were in favor of raising property taxes to fund the hiring of more statistics teachers. The resulting confidence interval. for the true proportion of residents in favor of raising taxes was (0.183,0.257). The margin of error for this confidence interval is

(a) 0.037

(b) 0.183

c) 0.220

(d) 0.257

(e) 0.740

Short Answer

Expert verified

The margin of error for this confidence interval is (a)0.037

Step by step solution

01

Given information

We are given that a school board selects a random sample and asked if they were in favor of raising property taxes to fund the hiring of more statistics teachers.

We need to find the margin of error for this confidence interval is.

02

Simplify

As given in the question,

The resulting confidence interval. for the true proportion of residents in favor of raising taxes was 0.183,0.257

As we know,

The resulting confidence interval :p^-MOE,p^+MOE

where,

MOE=margin of error

p^=true proportion

According to formula,

p^+MOE=0.257p^-MOE=0.183p^+MOE-p^-MOE=2×MOEMOE=0.257-0.1832=0.037

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