Estimating an Average of a Population

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.

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.

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 for 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.

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 to 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.