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Chapter 8: Q. T8.1 (page 549)

The Gallup Poll interviews 1600 people. Of these, 18% say that they jog regularly. The news report adds: “The poll had a margin of error of plus or minus three percentage points at a 95% confidence level.” You can safely conclude that

a. 95% of all Gallup Poll samples like this one give answers within ±3% of the true population value.

b. the percent of the population who jog is certain to be between 15% and 21%.

c. 95% of the population jog between 15% and 21% of the time.

d. we can be 95% confident that the sample proportion is captured by the confidence interval.

e. if Gallup took many samples, 95% of them would find that 18% of the people in the sample jog.

Short Answer

Expert verified

The required correct option is(b)

Step by step solution

01

Given information

The proportion of people that jog regularly (p^)=18%=0.18

Number of people (n)=1600

Margin of error(E)=3%=0.03

02

The objective is to draw the calculation using the provided information

The formula for calculating the confidence interval for a population proportion is as follows:

p^±E

The confidence interval can be computed as follows:
CI=p^±E=0.18±0.03=(0.15,0.21)

Using the above calculations, the true population proportion of people who jog could be estimated to be between15%and21%.

Therefore, the correct option is(b)

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