AP Statistics Sample Questions

A summer resort rents rowboats to customers but does not allow more than four people to a boat. Each boat is designed to hold no more than 800 pounds. Suppose the distribution of adult males who rent boats, including their clothes and gear, is normal with a mean of 190 pounds and standard deviation of 10 pounds. If the weights of individual passengers are independent, what is the probability that a group of four adult male passengers will exceed the acceptable weight limit of 800 pounds? (a) 0 .023 (b) 0 .046 (c) 0 .159 (d) 0 .317 (e) 0 .977

A

In a test of H0: μ=8 versus Ha: μ≠8, a sample of size 220 leads to a p-value of 0 .034. Which of the following must be true? (a) A 95% confidence interval for μ calculated from these data will not include μ = 8. (b) At the 5% level if H0 is rejected, the probability of a Type II error is 0 .034. (c) The 95% confidence interval for μ calculated from these data will be centered at μ = 8. (d) The null hypothesis should not be rejected at the 5% level. (e) The sample size is insufficient to draw a conclusion with 95% confidence.

A

A candy company claims that 10 percent of its candies are blue . A random sample of 200 of these candies is taken, and 16 are found to be blue . Which of the following tests would be most appropriate for establishing whether the candy company needs to change its claim? (a) Matched pairs t-test (b) One-sample propor tion z-test (c) Two-sample t-test (d) Two-sample proportion z-test (e) Chi-square test of association

B

All bags entering a research facility are screened. Ninety-seven percent of the bags that contain forbidden material trigger an alarm. Fifteen percent of the bags that do not contain forbidden material also trigger the alarm. If 1 out of every 1,000 bags entering the building contains forbidden material, what is the probability that a bag that triggers the alarm will actually contain forbidden material? (a) 0 .00097 (b) 0 .00640 (c) 0 .03000 (d) 0 .14550 (e) 0 .97000

B

In a certain game, a fair die is rolled and a player gains 20 points if the die shows a "6." If the die does not show a "6," the player loses 3 points. If the die were to be rolled 100 times, what would be the expected total gain or loss for the player? (a) A gain of about 1,700 points (b) A gain of about 583 points (c) A gain of about 83 points (d) A loss of about 250 points (e) A loss of about 300 points

C

TheAttila Barbell Company makes bars for weight lifting. The weights of the bars are independent and are normally distributed with a mean of 720 ounces (45 pounds) and a standard deviation of 4 ounces. The bars are shipped 10 in a box to the retailers. The weights of the empty boxes are normally distributed with a mean of 320 ounces and a standard deviation of 8 ounces. The weights of the boxes filled with 10 bars are expected to be normally distributed with a mean of 7,520 ounces and a standard deviation of (a) Square-root of 12 ounces (b) Square-root of 80 ounces (c) Square-root of 224 ounces (d) Square-root of 48 ounces (e) Square-root of 1,664 ounces

C

Under which of the following conditions is it preferable to use stratified random sampling rather than simple random sampling? 20 (a) The population can be divided into a large number of strata so that each stratum contains only a few individuals. (b) The population can be divided into a small number of strata so that each stratum contains a large number of individuals. (c) The population can be divided into strata so that the individuals in each stratum are as much alike as possible. (d) The population can be divided into strata so that the individuals in each stratum are as different as possible. (e) The population can be divided into strata of equal sizes so that each individual in the population still has the same chance of being selected.

C

Consider a data set of positive values, at least two of which are not equal . Which of the following sample statistics will be changed when each value in this data set is multiplied by a constant whose absolute value is greater than 1? I . Themean II . Themedian III . Thestandarddeviation (a) I only (b) II only (c) III only (d) I and II only (e) I, II, and III

E

Each person in a simple random sample of 2,000 received a survey, and 317 people returned their survey . How could nonresponse cause the results of the survey to be biased? (a) Those who did not respond reduced the sample size, and small samples have more bias than large samples. (b) Those who did not respond caused a violation of the assumption of independence. (c) Those who did not respond were indistinguishable from those who did not receive the survey. (d) Those who did not respond represent a stratum, changing the simple random sample into a stratified random sample. (e) Those who did respond may differ in some important way from those who did not respond.

E