Chapter 8: Q 30. (page 522)
High tuition costs Glenn wonders what proportion of the students at his college believe that tuition is too high. He interviews an SRS of of the students and finds of those interviewed think tuition is too high.
All the conditions are met in given case.
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The Large Counts condition When constructing a confidence interval for a population proportion, we check that both are at least
a. Why is it necessary to check this condition?
b. What happens to the capture rate if this condition is violated?
After deciding on a confidence level, the researcher is deciding between a sample of size and a sample of size . Compared with using a sample size of , a confidence interval based on a sample size of will be
a. narrower and would involve a larger risk of being incorrect.
b. wider and would involve a smaller risk of being incorrect.
c. narrower and would involve a smaller risk of being incorrect.
d. wider and would involve a larger risk of being incorrect.
e. narrower and would have the same risk of being incorrect.
A Gallup poll found that only 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 confidence level. This means that
a. the poll used a method that gets an answer within 3% of the truth about the population of the time.
b. the percent of all adults who expect an inheritance must be between and .
c. if Gallup takes another poll on this issue, the results of the second poll will lie between and .
d. there’s a 95% chance that the percent of all adults who expect an inheritance is between
25% and 31%.
e. Gallup can be 95% confident that between 25% and 31% of the sample expect an inheritance.
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. How much time do students at your school spend on the Internet? You collect data from the members of your AP Statistics class and calculate the mean amount of time that these students spent on the Internet yesterday.
b. Is the real-estate market heating up? To estimate the mean sales price, a realtor in a large city randomly selected home sales from the previous months in her city. These sales prices are displayed in the boxplot.
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.
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