AP Statistics Review #3

Are the five flavor of Skittles candies equally likely to be found in a large bag of regular Skittles? A student selected a random sample of Skittles from the large bag, verified the conditions for inference were met, performed a chi-square test, and got a P-value of 0.023. Which of the following could have been the test statistic?

• We cannot determine the value of the test statistic without the sample size.

Answer explanation

I would use the chi-square cdf function to test each value. Since there are 5 colors the degrees of freedom are 4.

Tags

CCSS.HSS.IC.A.1

The distribution of commute times for the employees at a large company is skewed to the right with a mean of 22 minutes and a standard deviation of 14 minutes. If a human resources director selects a random sample of 50 employees, which of the following is closest to the probability that the sample mean commute time is less than 20 minutes?

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.ID.A.4

CCSS.HSS.IC.B.4

Park rangers are interested in estimating the weight of the bears that inhabit their state. The rangers have data on weight (in pounds) and neck girth (distance around the neck in inches) for 10 randomly selected bears. Here is some computer output from a linear regression analysis of these data.

Which of the following represents a 95% confidence interval for the slope of the population least-squares regression line relating the weight of a bear and its neck girth, assuming the conditions for inference are met?

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.ID.C.7

A distribution of exam scores has a mean of 60 and a standard deviation of 18. If each score is doubled, and then 5 is subtracted from the result, what will the mean and standard deviation of new scores be?

• mean = 115
  standard deviation = 31

• mean = 115
  standard deviation = 36

• mean = 120
  standard deviation = 6

• mean = 120
  standard deviation = 31

• mean = 120
  standard deviation = 36

Tags

CCSS.HSS.ID.A.4

CCSS.HSS.ID.A.2

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

Suppose the population proportion of people who use public transportation to get to work in Washington, D.C., area is 0.45. In a simple random sample of 250 people who work in the city, about how far do you expect the sample proportion to be from the population proportion?

• 0.0010

• 0.0285

• 0.0315

• 0.4975

• 7.8661

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.MD.A.2

Why is random assignment an important part of a well-designed experiment?

• Because it eliminates chance variation in the results.

• Because it helps create roughly equivalent groups before treatments are imposed on subjects.

• Because it allows researchers to generalize the results of their experiment to a larger population.

• Because it helps to eliminate any possibility of bias in the experiment.

• Because it prevents the placebo effect from occuring.

Tags

CCSS.HSS.IC.B.3

A class of 20 students includes 14 seniors and 6 juniors. Each day, the teacher randomly selects an SRS of 4 students to present the answer to a homework question. Which of the following correctly describes one trial of a simulation to estimate the probability that all four chosen are juniors?

• Let 1 - 70 = senior and 71 - 100 = junior. Generate 4 random integers with replacement from 1 to 100 and count how many integers are between 71 and 100.

• Let 1 - 70 = senior and 71 - 100 = junior. Generate 4 random integers without replacement from 1 to 100 and count how many integers are between 71 and 100.

• Let 1 - 14 = senior and 15 - 20 = junior. Generate 4 random integers with replacement from 1 to 20 and count how many integers are between 15 and 20.

• Let 1 - 14 = senior and 15 - 20 = junior. Generate 4 random integers without replacement from 1 to 20 and count how many integers are between 15 and 20.

• Let 1 - 14 = senior and 15 - 20 = junior. Generate 6 random integers with replacement from 1 to 20 and count how many integers are between 15 and 20.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.3

CCSS.HSS.IC.B.4

CCSS.HSS.CP.A.1

• Because the population may not be normally distributed.

• Because the sample may not be normally distributed.

• Because we do not know the population mean.

• Because we do not know the sample standard deviation.

• Because we do not know the population standard deviation.

Answer explanation

The t-distribution uses the the sample standard deviation to estimate the standard deviation of the sampling distribution. For us it is a concept that if you know the population standard deviation then we can use a z-score.

Tags

CCSS.HSS.ID.A.4

CCSS.HSS.ID.A.2

• Yes, because a different fertilizer was used on each garden.

• Yes, because random samples were taken from each garden.

• Yes, because the P-value is so small.

• No, because the condition of the soil in the two gardens is a potential confounding variable.

Answer explanation

Plants will respond differently to different soil, so soil could be a confounding variable.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.3

CCSS.HSS.IC.B.5

CCSS.HSS.ID.C.9

The weights of chocolate truffles made by a candy shop are approximately normally distributed with a mean of 2 ounces and a standard deviation of 0.3 ounce.

a) What is the probability that a randomly selected chocolate truffle from this candy shop will weigh less than 1.5 ounces?

b) The candy shop assembles gift boxes that contain 8 randomly selected chocolate truffles. What is the probability that none of the truffles in a gift box weighs less than 1.5 ounces?

c) The weights of gift boxes, including all packaging materials, are approximately normally distributed with a mean of 3 ounces and a standard deviation of 0.5 ounce. If 8 randomly selected chocolate truffles are placed into a randomly selected gift box, describe the distribution of the total weight of the gift box and truffles.

Tags

CCSS.HSS.ID.A.4

CCSS.HSS.MD.A.3