AP Statistics Unit 7 MC Questions

One reason for using a t distribution instead of the standard Normal distribution 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 know the population standard deviation σ.
• z requires that you can regard your data as an SRS from the population.
• z requires that the sample size is less than 10% of the population size.
• a z critical value will lead to a wider interval than a t critical value.

The reason we use t procedures instead of z procedures when carrying out a test about a population mean is that

• z requires that the sample size be large.
• z requires that you know the population standard deviation σ.
• z requires that the data come from a random sample
• z requires that the population distribution be Normal.
• z can only be used for proportions.

• falls between 0.01 and 0.02.
• falls between 0.02 and 0.04.
• falls between 0.04 and 0.05.
• falls between 0.05 and 0.25.
• is greater than 0.25.

• t > 3.326
• 3 > 3.286
• t > 2.977
• t < -3.326 or t > 3.326
• t < -3.286 or t > 3.286

• A 95% confidence interval for μ will include the value 1.
• A 95% confidence interval for μ will include the value 0.022.
• A 99% confidence interval for μ will include the value 1.
• A 99% confidence interval for μ will include the value 0.022.
• None of these is necessarily true.

The most important condition for making an inference about a population mean from a significance test is that

• the data comes from a random sample.
• the population distribution is exactly Normal.
• the data contain no outliers.
• the sample size is less than 10% of the population.
• the sample size is at least 30.

Vigorous exercise helps people live several years longer (on average). Whether mild activities like slow walking extend life is not clear. Suppose that the added life expectancy from regular slow walking is just 2 months. A significance test is more likely to find a significant increase in mean life expectancy with regular slow walking if

• it is based on a very large random sample and a 5% significance level is used.
• it is based on a very large random sample and a 1% significance level is used.
• it is based on a very small random sample and a 5% significance level is used.
• it is based on a very small random sample and a 1% significance level is used.
• the size of the sample doesn’t have any effect on the significance of the test.

A 99% confidence interval for the mean sugar content (per 5 oz. serving) of a shipment of strawberries is 5.9 to 8.3 grams. What are the values of the point estimate and the margin of error for this confidence interval?

• Point estimate = 5.9; Margin of error = 2.4
• Point estimate = 5.9; Margin of error = 1.2
• Point estimate = 7.1; Margin of error = 2.4
• Point estimate = 7.1; Margin of error = 1.2
• Point estimate = 8.3; Margin of error = 2.4

A 99% confidence interval for the mean sugar content (per 5 oz. serving) of a shipment of strawberries is 5.9 to 8.3 grams. Which one of the following is the best interpretation of the 99% confidence level for the mean sugar content of the shipment?

• There is a 99% probability that the true mean sugar content of the strawberries in the shipment is between 5.9 and 8.3 grams.
• There is a 99% probability that the interval 5.9 to 8.3 has captured the true mean.
• If we constructed many, many confidence intervals from random samples of this size, approximately 99% of the time the true mean would be between 5.9 and 8.3 grams.
• If we constructed many, many confidence intervals from random samples of this size, approximately 99% of the intervals we constructed would capture the true population mean.
• If we constructed many, many confidence intervals from random samples of this size, approximately 99% of the intervals we constructed would capture the sample mean.

A 99% confidence interval for the mean sugar content (per 5 oz. serving) of a shipment of strawberries is 5.9 to 8.3 grams. If we chose to calculate a 95% confidence interval using the same data instead of calculating a 99% confidence interval, which of the following would describe the change in width of the interval?

• It would be wider.
• It would be narrower.
• The margin of error would be the same, but the center of the interval would be different.
• It would have the same margin of error and same center.
• Because the sample mean is a random variable, we cannot predict how the 95% confidence interval would change.