AP Stats Chapter 8

A researcher plans to use a random sample of n = 500 families to estimate the mean monthly family income for a large population. A 99% confidence interval based on the sample would be _____ than a 90% confidence interval.

• narrower and would involve a larger risk of being incorrect

• wider and would involve a smaller risk of being incorrect

• narrower and would involve a smaller risk of being incorrect

• wider and would involve a larger risk of being incorrect

• wider, but it cannot be determined whether the risk of being incorrect would be larger or smaller

In a 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 for the poll?

• I only

• II only

• III only

• I, II, and III

• None of these

You have measured the systolic blood pressure of an SRS of 25 company employees. A 95% confidence interval for the mean systolic blood pressure for the employees of this company is (122, 138). Which of the following statements gives a valid interpretation of this interval?

• 95% of the sample of employees have a systolic blood pressure between 122 and 138.

• 95% of the population of employees have a systolic blood pressure between 122 and 138.

• If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.

• The probability that the population mean blood pressure is between 122 and 138 is 0.95.

• If the procedure were repeated many times, 95% of the sample means would be between 122 and 138.

A polling organization announces that the proportion of American voters who favor congressional term limits is 64%, with a 95% confidence margin of error of 3%. If the opinion poll had announced the margin of error for 80% confidence rather than 95% confidence, this margin of error would be

• 3%, because the same sample is used.

• less than 3%, because we require less confidence.

• less than 3%, because the sample size is smaller.

• greater than 3%, because we require less confidence.

• greater than 3%, because the sample size is smaller.

A Gallup Poll found that only 28% of American adults expect to inherit money or valuable possessions from a relative. The poll’s margin of error was ±3 percentage points at a 95% confidence level. This means that

• the poll used a method that gets an answer within 3% of the truth about the population 95% of the time.

• the percent of all adults who expect an inheritance is between 25% and 31%.

• if Gallup takes another poll on this issue, the results of the second poll will lie between 25% and 31%.

• there’s a 95% chance that the percent of all adults who expect an inheritance is between 25% and 31%.

• Gallup can be 95% confident that between 25% and 31% of the sample expect an inheritance

Most people can roll their tongues, but many can’t. The ability to roll the tongue is genetically determined. Suppose we are interested in determining what proportion of students can roll their tongues. We test a simple random sample of 400 students and find that 317 can roll their tongues. The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to

• 0.008.

• 0.02.

• 0.03.

• 0.04.

• 0.208.

You want to design a study to estimate the proportion of students at your school who agree with the statement, “The student government is an effective organization for expressing the needs of students to the administration.” You will use a 95% confidence interval, and you would like the margin of error to be 0.05 or less. The minimum sample size required is

• 22.

• 271.

• 385.

• 769.

• 1795.

I collect an SRS of size n from a population and compute a 95% confidence interval for the population proportion. Which of the following would produce a new confidence interval with larger width (larger margin of error) based on these same data?

• Use a larger confidence level.

• Use a smaller confidence level.

• Increase the sample size.

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

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

One reason for using a t distribution instead of the standard Normal curve to find critical values when calculating a level C confidence interval for a population mean is that

• z can be used only for large samples.

• z requires that you know the population standard deviation σ.

• z requires that you can regard your data as an SRS from the population.

• the standard Normal table doesn’t include confidence levels at the bottom.

• a z critical value will lead to a wider interval than a t critical value.

You have an SRS of 23 observations from a Normally distributed population. What critical value would you use to obtain a 98% confidence interval for the mean μ of the population if σ is unknown?

• 2.508

• 2.500

• 2.326

• 2.183

• 2.177