Chapter 8 MC

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.

The weights (in pounds) of three adult males are 160, 215, and 195.

What is the standard error of the mean for these data?

• 16.07

• 
  27.84

• 
  13.13

• 
  22.73

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 𝑛𝑜𝑡not be safe constructing the interval based on an SRS of size 14 from the population?

• A boxplot shows that the values above the median are much more variable than the values below the median.

• A histogram of the data shows slight skewness.

• The sample standard deviation is large.

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

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 true proportion 𝑝 of all 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?

• 700

• 600

• 650

• 750

You want to compute a 90% confidence interval for the mean of a population with an unknown population standard deviation. The sample size is 30.

What critical value should you use for this interval?

• 1.699

• 
  

  1.645

• 
  1.697

• 
  

  2.045

A radio talk show host with a large audience is interested in the proportion 𝑝p 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 18-year-olds are eligible for military service?” He asks listeners to go to his website and vote “Yes” if they agree the drinking age should be lowered and “No” if not. Of the 100 people who voted, 70 answered “Yes.”

Which of the following conditions are violated?

I. Random
II. 10%
III. Large Counts

• I only

• III only

• I and II only

• I, II and III

A 90% confidence interval for the mean 𝜇 of a population is computed from a random sample and is found to be 90 ± 30.

Which of the following 𝑐𝑜𝑢𝑙𝑑 be the 95% confidence interval based on the same data?

• 90 ± 39

• 90 ± 30

• 
  90 ± 21

• 
  

  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 at most $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 which of the following?

• 609

• 30

• 225

• 867

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?

• No; the margin of error only accounts for sampling variability.

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

• Yes; the margin of error accounts for undercoverage but not nonresponse.

• 
  No; the margin of error accounts for nonresponse but not undercoverage.

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 $57,005 with a margin of error of $742.

Which of the following is the most appropriate conclusion?

• The Census Bureau got the result $57,005 ± $742 using a method that will capture the true median income 90% of the time when used repeatedly.

• We can be sure that the median income for all households in the country lies in the interval $57,005 ± $742.

• 90% of the households in the sample interviewed by the Census Bureau had incomes in the interval $57,005 ± $742.

• 90% of all possible samples of this same size would result in a sample median that falls within $742 of $57,005.