AP Statistics Chapter 9

A researcher plans to use a random sample of families to estimate the mean monthly family income for a large population. The researcher is deciding between a 95% confidence level and a 99% confidence level. Compared to a 95% confidence interval, a 99% confidence interval will be…

• It would be narrower because it omits only 1% of the possible samples instead of 5%

• It would be wider because it has a higher confidence, which requires a larger margin of error.

• It would be narrower because it has a higher confidence, which requires a larger margin of error.

• It would be the same because the sample is the same.

• You can’t tell because the margin of error varies from sample to sample.

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…

• 95% of all Gallup Poll samples like this one give answers within ±3% of the true population value.

• The percent of the population who jog is certain to between 15% and 21%.

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

• We can be 95% confident that the sample proportion is captured by the confidence interval.

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

The weights (in pounds) of three adult males are 160, 215, and 195. The standard error of the mean of these three weights is…

• 190

• 27.84

• 22.73

• 16.07

• 13.13

One reason for using a t distribution instead of 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 ơ.

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

• Z requires that the sample size is at most 10% of the population size.

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

What conditions are NOT necessary for a 95% t interval with a sample size of 9 to be valid?

• The sample was selected randomly from the population of interest.

• The population standard deviation is not known.

• It is reasonable to assume that the population is approximately normal.

• n*p-hat > 10 and n(1 - p-hat) > 10

• All of the above are necessary conditions.

In preparing to construct a one-sample t interval for a population mean, suppose we are not sure if the population distribution is Normal. In which of the following circumstances would we not be safe constructing the interval based on an SRS of size 24 of the population?

• A stemplot of the data is roughly bell-shaped.

• A histogram of the data shows slight skewness.

• A boxplot of the data has a large outlier.

• The sample standard deviation is large.

• A Normal probability plot of the data is fairly linear.

You want to compute a 90% confidence interval for the mean of a population with unknown population standard deviation. The sample size is 30. The value of t* you would use for this interval is…

• 1.645

• 1.699

• 1.697

• 1.96

• 2.045

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 eighteen-year-olds are eligible for military service?” He asks listeners to phone in and vote “Yes” if they agree the drinking age should be lowered and “No” if not. Of the 100 people who phoned in, 70 answered “Yes”. Which of the following conditions for inference about a proportion using a confidence interval are violated?

• I only

• II only

• III only

• I and II only

• I, II and III

Suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their first year at a major university. The interval is to have a margin of error of $2. Based on last year’s book sales, we estimate that the standard deviation of the amount spent will be close to $30. The minimum sample size required is closest to…

• 25

• 30

• 608

• 609

• 865

A Census Bureau report on the income of Americans says that with 90% confidence the median income of all U.S. households in a recent year was $57005 with a margin of error of ±$742. This means that…

• 90% of all households had incomes in the range of $57005 ± $742.

• We can be sure that the median income for all households in the country lies in the interval $57005 ± $742

• 90% of the households in the sample interviewed by the Census Bureau had incomes in the interval $57005 ± $742.

• The Census Bureau got the result $57005 ± $742 using a method that will capture the true median income 90% of the time when used repeatedly.

• 90% of all possible samples of this same size would result in a sample median that falls with $742 of $57005.