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Chapter 8: Q 33. (page 522)

The 10%condition When constructing a confidence interval for a population proportion, we check that the sample size is less than 10%of the population size.

a. Why is it necessary to check this condition?

b. What happens to the capture rate if this condition is violated?

Short Answer

Expert verified

a. If sample size is less than 10%of population, observations are closer to independent.

b. The confidence interval will be inaccurate.

Step by step solution

01

Given Information

When constructing a confidence interval for a population proportion, it is checked that sample size is less than 10% of population size.

02

Necessity of this Condition

This condition is important due to the the fact that when sample size is less than 10%of population size, observations are closer to independent.

If this requirement is not met, it is not possible to calculate standard deviation of distribution.

03

If Population Size is not less than 10%

If this requirement is not met, it is not possible to calculate standard deviation of distribution correctly.

If standard deviation is not correct, confidence level will be inaccurate. There are less chances to obtain population parameter in confidence interval.

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Most popular questions from this chapter

Batteries A company that produces AA batteries tests the lifetime of a randomsample of 30 batteries using a special device designed to imitate real-world use. Based onthe testing, the company makes the following statement: “Our AA batteries last an average of 430 to 470 minutes, and our confidence in that interval is 95%.”36

a. Determine the point estimate, margin of error, standard error, and sample standard

deviation.

b. A reporter translates the statistical announcement into “plain English” as follows: “95% of this company’s AA batteries last between 430 and 470 minutes.” Comment on this interpretation.

c. Your friend, who has just started studying statistics, claims that there is a 95% probability that the mean lifetime will fall between 430 and 470 minutes. Do you agree? Explain your reasoning.

d. Give a statistically correct interpretation of the confidence level that could be published in a newspaper report.

Check them all Determine if the conditions are met for constructing a confidence interval for the population mean in each of the following settings.

a. We want to estimate the average age at which U.S. presidents have died. So we obtain a list of all U.S. presidents who have died and their ages at death.

b. Do teens text more than they call? To find out, an AP Statistics class at a large high school collected data on the number of text messages and calls sent or received by each of 25randomly selected students. The boxplot displays the difference (Texts − Calls) for each student.

Pepperoni pizza Melissa and Madeline love pepperoni pizza, but sometimes they are disappointed with the small number of pepperonis on their pizza. To

investigate, they went to their favorite pizza restaurant at 10 random times during the week and ordered a large pepperoni pizza. Here are the number of pepperonis on each pizza:

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.

Age and September 11 Refer to Exercise 42. The study also reported that 86% of

millennials included 9/11 in their top-10 list and 70% of baby boomers included 9/11.

a. Explain why you do not have enough information to give confidence intervals for

millennials and baby boomers separately.

b. Do you think a 95%confidence interval for baby boomers would have a larger or smaller margin of error than the estimate from Exercise 42? Explain your answer.
See all solutions

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