Advanced Placement Exam On Statistics! Trivia Questions Quiz

1.

A set of test scores has the following 5-number summary: Min Q1 Median Q3 Max 2 18 22.5 28.5 33 Which statement about outliers must be true?

A.

There is exactly one outlier on the lower end.
B.

There is at least one outlier on the lower end.
C.

There is exactly one outlier on the higher end.
D.

There is at least one outlier on the higher end.
E.

There are no outliers.

Correct Answer
B. There is at least one outlier on the lower end.

Explanation
Based on the given 5-number summary, the minimum value is 2, which is lower than the lower quartile (Q1) value of 18. This indicates that there is at least one data point that is significantly lower than the majority of the data, making it an outlier on the lower end. Therefore, the statement "There is at least one outlier on the lower end" is true.

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2.

The table below shows the regression output for predicting the number of calories from the number of milligrams of sodium for items at a fast-food chain. What percent of the variation in calories is explained by the regression model using sodium as a predictor?

A.

7.36%
B.

54.2%
C.

53.8%
D.

73.4%
E.

73.6%

Correct Answer
B. 54.2%

Explanation
The correct answer is 54.2%. In regression analysis, the coefficient of determination (R-squared) represents the proportion of the variation in the dependent variable (calories) that can be explained by the independent variable (sodium). Therefore, 54.2% of the variation in calories can be explained by the regression model using sodium as a predictor.

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3.

Marine biologists want to determine whether a small increase in acidity of sea water would adversely affect marine life. They randomly assigned several Entacmaea quadricolor (a type of sea anemone), to one of eight aquariums with environments as similar as possible to the natural habitat. Then they randomly selected four tanks, and gradually increased the acidity of the water. They monitored the health of the anemones for the duration of the study. Which is not true about this study?

A.

An advantage of using only one variety of sea anemones is that there should be less variability in the response to each treatment.
B.

A disadvantage of using only one variety of sea anemones is that the scope of inference is limited only to that type of anemone.
C.

An advantage of using aquariums is that it is easier to maintain control to avoid confounding factors.
D.

A disadvantage of using aquariums is that the anemones might respond differently in the ocean than they do in the aquariums.
E.

If the anemones in the aquariums with increased acidity are less healthy than those without increased acidity, it cannot be determined that the increased acidity caused the response.

Correct Answer
E. If the anemones in the aquariums with increased acidity are less healthy than those without increased acidity, it cannot be determined that the increased acidity caused the response.

Explanation
The statement that if the anemones in the aquariums with increased acidity are less healthy than those without increased acidity, it cannot be determined that the increased acidity caused the response is not true about this study. This is because the researchers randomly assigned the sea anemones to different aquariums and gradually increased the acidity in only four of the tanks. By comparing the health of the anemones in the tanks with increased acidity to those without increased acidity, the researchers can establish a causal relationship between the increased acidity and the adverse effects on marine life.

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4.

A polling company wants to estimate, using a 95% confidence interval, the proportion of likely voters that would vote for a particular candidate in the upcoming election. Of the following choices, which is the smallest sample size that will ensure a margin of sampling error less than or equal to 2 percentage points?

A.

250
B.

950
C.

1,150
D.

2,250
E.

2,450

Correct Answer
E. 2,450

Explanation
To ensure a margin of sampling error less than or equal to 2 percentage points, a larger sample size is required. The larger the sample size, the smaller the margin of error. Among the given choices, 2,450 is the largest sample size, which means it will provide a smaller margin of error compared to the other options. Therefore, 2,450 is the smallest sample size that will ensure a margin of sampling error less than or equal to 2 percentage points.

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5.

A multiple choice test has 30 questions, and each question has five options. A student has not studied and will guess on every question. Which calculation shows how to find the probability of getting 15 or more questions correct?

A.

A
B.

B
C.

C
D.

D
E.

E

Correct Answer
A. A

Explanation
To find the probability of getting 15 or more questions correct, we need to calculate the probability of getting exactly 15, 16, 17, ..., or 30 questions correct and add them together. Since each question has 5 options and the student is guessing, the probability of getting a question correct is 1/5. Therefore, the calculation to find the probability is (1/5)^15 + (1/5)^16 + (1/5)^17 + ... + (1/5)^30.

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