Estimating a Population Mean

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

• 190

• 27.84

• 22.73

• 16.07

• 13.13

We want to construct a one-sample t interval for a population mean using data from a population with unknown shape. In which of the following circumstances would it be inappropriate to construct the interval based on an SRS of size 14 from the population?

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

• A histogram of the data shows slight skewness.

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

• The sample standard deviation is large.

• The sample standard deviation is small.

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 ± 21

• 90 ± 30

• 90 ± 39

• 90 ± 70

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

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?

• 90% of all households had incomes in the interval $ 57 , 005 ± $ 742 .

• 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 .

• 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.

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

The makers of a specialty brand of bottled water claim that their “mini” bottles contain 8 ounces of water. To investigate this claim, a consumer advocate randomly selected a sample of 10 bottles and carefully measured the amount of water in each bottle. The mean volume was 7.98 ounces and the 95% confidence interval for true mean volume is 7.93 to 8.03 ounces. Based on the sample, which of the following conclusions best addresses the makers’ claim?

• Because 7.98 is in the interval, there is convincing evidence that their claim is correct.

• Because 7.98 is in the interval, there is not convincing evidence that their claim is incorrect.

• Because 8 is in the interval, there is convincing evidence that their claim is correct.

• Because 8 is in the interval, there is not convincing evidence that their claim is incorrect.

• Because 0 is not the interval, there is convincing evidence that their claim is incorrect.