Chapter 8 Review - Confidence Intervals for Proportions

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

• the percent of the population who jog is certain to be between 15% and 21%,

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

• 95% of all Gallup Poll samples like this one give answers within ±3%

  ±3% of the true proportion value.

• we can be 3% confident that the sample result is true.

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

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CCSS.HSS.IC.B.4

You are told that the proportion of those who answered "yes" to a poll about internet use is 0.70, and that the standard error is 0.0459. The sample size

• can not be determined from the information given.

• is 100.

• is 200.

• is 99.

• is 50.

I collect a random sample of size n from a population and from the data collected compute a 95% confidence interval for the mean of the population. Which of the following would produce a wider confidence interval, based on these same data?

• Use a larger confidence level

• Use a smaller confidence level

• Nothing can ensure that you will get a larger interval. One can only say the chance of obtaining a larger interval is 0.05.

• Nothing can ensure that you will get a larger interval. One can only say the chance of obtaining a smaller interval is 0.05.

• Use the same confidence level, but compute the interval n times. Approximately 5% of these intervals will be larger.

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CCSS.HSS.IC.B.4

A sample survey interviews SRSs of 500 female college students and 550 male college students. Each student is asked whether he or she worked for pay last summer. In all, 410 of the women and 484 of the men say "yes". The 95% confidence interval for the difference 

 $p_M-p_F$  

• −0.06 ± 0.043

• 0.06 ± 0.00095

• 0.06 ± 0.036

• 0.06 ± 0.043

• −0.06 ± 0.036

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CCSS.HSS.IC.B.4

A marketing company discovered the following problems with a recent poll:

I. Some people refused to answer questions.

II. People without telephones could not be in the sample.

III. Some people never answered the phone in several calls.

Which of these sources is included in the ±2% margin of error announced in the poll?

• Only source I

• Only source II

• Only source III

• All three sources

• None of these are sources of error.

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CCSS.HSS.IC.B.4