Inferences for Means

One reason for using a t distribution instead of the 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 can regard your data as an SRS from the population

• z requires that the sample size is at most

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

You have an SRS of 23 observations from large population. The distribution of sample values is roughly symmetric with no outliers. What critical value would you use to obtain a 98% confidence interval for the mean of the population?

• 2.177

• 2.183

• 2.326

• 2.500

• 2.508

A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production. Which of the following would result in the smallest margin of error in estimating the mean salt content σ ?

• 90% confidence; n = 25 

• 90% confidence; n = 50 

• 95% confidence; n =25 

• 95% confidence; n =50 

• n=100 at any confidence level 

Scientists collect data on the blood cholesterol levels (milligrams per deciliter of blood) of a random sample of 25 laboratory rats. A 95% confidence interval for the mean blood cholesterol level μ is 80.2 to 89.8. Which of the following would cause the most worry about the validity of this interval?

• There is a clear outlier in the data

• A stemplot of the data shows a mild right skew

• You do not know the population standard deviation σ

• The population distribution is not exactly Normal.

• None of these are a problem when using t-interval

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

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 90% confidence interval for the mean µ 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 Census Bureau report on the income of Americans says that with 90% confidence the mean income of all US 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