Chapter 8 Review

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 be 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

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 from the population?

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

• A histogram of the data shows slight skewness.

• A stemplot of the data has a large outlier.

• The sample standard deviation is large.

• The t procedures are robust, so it is always safe.

Many television viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, Timex Group USA wishes to estimate the proportion of consumers who believe what is shown in Timex television commercials. Let p represent the true proportion of consumers who believe what is shown in Timex television commercials. What is the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05 or less at a 99% confidence level?

• 550

• 600

• 650

• 700

• 750

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. The data are a random sample from the population of interest.

II. n is so large that both npˆ and n(1-pˆ) are at least 10.

III. The population is at least 10 times as large as the sample.

• I only

• II only

• III only

• I and II only

• I, II, and III

A 90% confidence interval for the mean of a population

is computed from a random sample and is found to

be 9 +/- 3. Which of the following could be the 95% confidence

interval based on the same data?

• 9 +/- 1.96

• 9 +/- 2

• 9 +/- 3

• 9 +/-4

• Without knowing the sample size, any of the above answers could be the 95% confidence interval.

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 number of observations required is closest to

• 25

• 30

• 608

• 609

• 865

A telephone poll of an SRS of 1234 adults found that 62% are generally satisfied with their lives. The announced margin of error for the poll was 3%. Does the margin of error account for the fact that some adults do not have telephones?

• Yes. The margin of error includes all sources of error in the poll.

• Yes. Taking an SRS eliminates any possible bias in estimating the population proportion.

• Yes. The margin of error includes undercoverage but not nonresponse.

• No. The margin of error includes nonresponse but not undercoverage.

• No. The margin of error only includes sampling variability.

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 $57,005 with a margin of error of +/- $742. This means that

• 90% of all households had incomes in the range $57,005 +/- $742.

• we can be sure that the median income for all households in the country lies in the range $57,005 +/- $742.

• 90% of the households in the sample interviewed by the Census Bureau had incomes in the range $57,005 +/- $742.

• the Census Bureau got the result $57,005 +/- $742 using a method that will cover 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 within $742 of $57,005.