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Chapter 8: Q 52. (page 523)

Election polling Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. We want to estimate the proportion p of all registered voters in the city who plan to vote for Chavez with 95%confidence and a margin of error no greater than 0.03. How large a random sample do we need?

Short Answer

Expert verified

Sample Size isn=1068

Step by step solution

01

Given Information

It is given that

Confidence Level =95%

E=0.03

Corresponding to95%, using tablesZα2=1.96

02

Concept Used

Formula to be used:

n=p^(1-p^)zaE2

03

Calculation 

Putting all values. sample size is calculated as:

=0.50(1-0.50)1.960.032

=1067.111

≈1068

Hence, sample size is1068

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Most popular questions from this chapter

Prom totals Use your interval from Exercise 39 to construct and interpret a 90%

confidence interval for the total number of seniors planning to go to the prom.

Willows in Yellowstone Writers in some fields summarize data by giving x ̄ and its

standard error rather than x¯andSX.Biologists studying willow plants in Yellowstone National Park reported their results in a table with columns labeled x¯andSX The table entry for the heights of willow plants (in centimeters) in one region of the park was 61.55±19.03. The researchers measured a total of 23plants.

a. Find the sample standard deviation sxfor these measurements.

b. A hasty reader believes that the interval given in the table is a 95% confidence interval for the mean height of willow plants in this region of the park. Find the actual confidence level for the given interval.

A radio talk show host with a large audience is interested in the proportion p of adults in his listening area who think the drinking age should be lowered to eighteen. To find this out, he poses the following question to his listeners: “Do you think that the drinking age should be reduced to eighteen in light of the fact that 18-year-olds are eligible for military service?” He asks listeners to go to his website and vote “Yes” if they agree the drinking age should be lowered and “No” if not. Of the 100 people who voted, 70 answered “Yes.” Which of the following conditions are violated?

I. Random

II. 10%

III. Large Counts

a. I only

b. II only

c. III only

d. I and II only

e. I, II, and III

More weight loss Refer to Exercise 6. Interpret the confidence level.

It’s about ME Explain how each of the following would affect the margin of error of a confidence interval, if all other things remained the same.

a. Increasing the confidence level

b. Quadrupling the sample size
See all solutions

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