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Chapter 8: Q.12 (page 477)

Suppose the Census needed to be 98% confident of the population mean length of time. Would the Census have to survey more people? Why or why not?

Short Answer

Expert verified

It is not required for the census to survey a larger number of people because the level of confidence does not depend on the sample size.

Step by step solution

01

Given Information

n=samplesize=200

x=Samplemean=8.2

σ=Populationstandarddeviation=2.2

02

Explanation

We are increasing the confidence level from 90% to 98%.

However, we have not been given whether they want to keep the error bound the same or not.

If they want to keep the error bound the same, then the Census will need to survey more people (as increasing the confidence level will increases the error bound and increasing the sample size will decreases the error bound again).

If they do not want to keep the error bound the same, then the sample size doesn't need to be increased and thus we don't require more people in the survey (as the error bound will simply increase).

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Most popular questions from this chapter

The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X=the age of a Winter Foothill College student.

role="math" localid="1648389122287" n=____

What will happen to the confidence interval obtained, if 500 newborn elephants are weighed instead of 50? Why ?

A student polls his school to see if students in the school district are for or against the new legislation regarding school uniforms. She surveys 600students and finds that 480are against the new legislation.

a. Compute a 90% confidence interval for the true percent of students who are against the new legislation, and interpret the confidence interval.

b.In a sample of 300students,68% said they own an iPod and a smartphone. Compute a 97% confidence interval for the true percent of students who own an iPod and a smartphone.

The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X=the age of a Winter Foothill College student.

As a result of your answer to Exercise 8.26, state the exact distribution to use when calculating the confidence interval.

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What would happen if 40 heads of lettuce were sampled instead of 20, and the confidence level remained the same?
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