AP Stats Review 7/8

Find the confidence interval for a mean of 142.5 and a margin of error of 5.2.

• (5.2, 142.5)

• (137.5, 142.5)

• (142.5, 147.5)

• (137.3, 147.7)

A sample of 20 cupcakes found the interval for average calories to be (150, 350). Which is the correct interpretation of the 95% confidence interval?

• We are 95% confident that the true mean caloric content can be found with a sample of 150 to 350 cupcakes.

• We are 95% confident that the interval (150, 350) captures the true average caloric content.

• We are 95% confident that a sample of 20 cupcakes will find 250 calories per cupcake.

• None of these are correct.

If using a 95% confidence level, what value of z should you use?

If using a 99% confidence level, what value of z should you use?

A large sample has mean of 7.1 and Standard Error of 2.3.

Construct a 90% Confidence Interval for the population mean µ (to two decimal places).

• (3.32, 10.88)

• (3.8, 7.1)

• (3.3, 10.9)

• (3.3165, 10.8835)

The lifetime of a certain type of batter is known to be normally distributed with a standard deviation of 20 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 99% confidence interval for the mean lifetime of this type of battery.

What is the Confidence Interval to one decimal place?

• (114.5, 125.6)

• (112.8, 127.4)

• (112.82, 127.38)

• (114.56, 125.64)

A survey of 121 subjects found that 84 have suffered the symptoms of depression in the last year. Calculate a 90% confidence interval for p.

• (0.612, 0.776)

• (0.641, 0.748)

• (0.780, 0.900)

• (0.621, 0.759)

Agricultural researchers plant 100 plots with a new variety of corn and measure the mean yield for these plots in bushels per acre. They treat the 100 plots as a simple random sample of possible plots of corn (as researchers often do) and report a 95% confidence interval for the mean corn yield of (128.4, 131.6) bushels per acre. Which of the following is a correct interpretation of the 95% confidence level?

• We are 95% confident that the true mean yield for this new variety of corn is captured by the interval (128.4, 131.6) bushels per acre
• If many intervals were constructed this way from many independent sets of 100 plots, 95% of the intervals would capture the true mean corn yield.
• If many intervals were constructed this way from many independent sets of 100 plots, 95% of the time the true mean corn yield would be in the interval (128.4, 131.6) bushels per acre.