AP Statistics Chapter 5 Review

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

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.

You want to calculate a 94% confidence interval for a population proportion from a sample of n = 38. What is the appropriate critical z*?

• 1.555, -1.555

• 1.881, -1.881

• 1.94, -1.94

• 1.592, -1.592

The probability that an American household will have at least 2 cars is...

• 0.55

• 0.35

• 0.45

• 0.93

The standard deviation of X is o_x = 1.08. If many households were selected at random, which of the following would be the best interpretation of the value 1.08?

• The mean number of cars would be about 1.08.

• If we randomly selected many households, the number of cars would typically vary be about 1.08 cars from the mean.

• The number of cars would be at most 1.08 from the mean.

• The number of cars would be within 1.08 from the mean about 68% of the time.

• The mean number of cars would be about 1.08 from the expected value.