AP Stats: Chapters 8 - 10 Review

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.

An inspector monitors large truckloads of potatoes to determine the proportion p of potatoes with major defects before the potatoes are used to make potato chips. She intends to compute a 95% confidence interval for p. To do so, she selects a simple random sample of 50 potatoes from a truckload of more than 2000 potatoes. Suppose that only 2 of the 50 potatoes sampled are found to have major defects. Which one of the following assumptions for inference about a proportion using a confidence interval is violated?

• Large counts.
• 10% condition.
• There are not violations.

A noted psychic is tested for extrasensory perception. The psychic is presented, one at a time, with cards that are marked with one of four symbols: a star, a cross, a circle, or a square. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. Which of the following is the smallest number of trials you would have to conduct to estimate p to within ± 0.01 with 95% confidence? (Use the guess 0.25 as the value for p, since this would be the value of p if the psychic were merely guessing.)

• 352
• 7203
• 9604

To assess the accuracy of a kitchen scale, a standard weight, known to weigh 1.000 gram, is weighed a total of n times, and the mean of the n weight measurements is computed. (If a 90% confidence interval for the mean calculated from these measurements does not contain 1.000, the scale is deemed inaccurate.) Suppose the scale readings are Normally distributed and that similar scales are known to measure such weights with a standard deviation of σ = 0.01 gram. Which of the following is the smallest value of n that will produce a 90% confidence interval with a margin of error of at most 0.001 grams?

• 17
• 271
• 385

Which one of the following statements is true about Student's t distribution?

• The density curve of the t distribution is symmetric and centered at the true mean of the population.
• The density curve of the t distribution has heavier “tails” than the density curve of the standard Normal distribution.
• The density curve of the t distribution more closely resembles the density curve of the standard Normal distribution when the number of degrees of freedom is small.

The heights (in inches) of adult males on a small Pacific Island are believed to be Normally distributed with an unknown mean μ. The average height of a random sample of 25 adult males from the island is found to be 69.72 inches, with a sample standard deviation of s = 4.15 inches. A 99% confidence interval for μ is

• 69.72 ± 2.32.
• 69.72 ± 2.07.
• 69.72 ± 11.61

The weight of the average 6th grade student's backpack (with books in it) is 18.4 lbs. The principal of the school thinks that the backpack does not weight 18.4 lbs. What is the null and alternate hypothesis? 

• H₀ = 18.4
  H_a = 18.4
• H₀ = 18.4
  H_a > 18.4
• H₀ = 18.4
  H_a < 18.4
• H₀ = 18.4
  H_a ≠ 18.4

• A
• B
• C
• D

• A
• B
• C
• D

• A
• B
• C
• D