Advanced Placement: Statistics Exam! Trivia Questions Quiz

1. Sixty-two students were asked to complete a number puzzle. The number of minutes each student needed to complete the puzzle was recorded and the times are displayed in the histogram below. Which of the following describes the distribution?

The distribution is approximately normal.

The distribution is roughly symmetric.

The distribution is bimodal.

The distribution is skewed left.

The distribution is skewed right.

The distribution is skewed left because the majority of the data is concentrated towards the right side of the histogram, with a longer tail on the left side. This indicates that there are fewer students who took a longer time to complete the puzzle, while a larger number of students completed it in a shorter amount of time.

Explanation

The distribution is skewed left because the majority of the data is concentrated towards the right side of the histogram, with a longer tail on the left side. This indicates that there are fewer students who took a longer time to complete the puzzle, while a larger number of students completed it in a shorter amount of time.

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. Which is a correct interpretation of the slope of the regression line?

Every milligram of sodium contains 0.2457 calories.

A food item with one more milligram of sodium than another tends to have 0.2457 more calories.

A food item with one more milligram of sodium than another tends to have 136.69 more calories.

A food item with one more milligram of sodium than another tends to have 147.1427 more calories.

A food item with one more calorie than another tends to have 147.1427 more milligrams of sodium.

The correct interpretation of the slope of the regression line is that every milligram of sodium contains 0.2457 calories. This means that for every additional milligram of sodium in a food item, there is an expected increase of 0.2457 calories.

Explanation

The correct interpretation of the slope of the regression line is that every milligram of sodium contains 0.2457 calories. This means that for every additional milligram of sodium in a food item, there is an expected increase of 0.2457 calories.

3. At a large hospital, the durations of emergency room visits, from check-in to discharge, are approximately normally distributed with a mean of 167 minutes and a standard deviation of 76 minutes. Which interval to the nearest minute, contains the middle 80% of durations?

15 minutes to 319 minutes

53 minutes to 281 minutes

70 minutes to 264 minutes

91 minutes to 243 minutes

103 minutes to 231 minutes

The middle 80% of durations refers to the range that contains the middle 80% of the data. In a normal distribution, this range is usually defined as the interval between the mean plus and minus 1.28 standard deviations. In this case, the mean is 167 minutes and the standard deviation is 76 minutes. Adding and subtracting 1.28 standard deviations to the mean gives us a range of approximately 70 minutes to 264 minutes, which is the correct answer.

Explanation

The middle 80% of durations refers to the range that contains the middle 80% of the data. In a normal distribution, this range is usually defined as the interval between the mean plus and minus 1.28 standard deviations. In this case, the mean is 167 minutes and the standard deviation is 76 minutes. Adding and subtracting 1.28 standard deviations to the mean gives us a range of approximately 70 minutes to 264 minutes, which is the correct answer.

4. Biologists have two different methods for estimating the growth rate of a population of animals. One is based on counting the number of animals in a photographic image, and the other is based on a computer-calculated surface area of the animals in the image. (Larger animals are generally older and contribute more to reproduction.) The scatterplot below shows the estimates of the Population Growth Rate (PGR) for each method along with the line y = x. Which statement is true based on the scatterplot.

The surface area method overestimates the Population Growth Rate.

The count method underestimates the Population Growth Rate.

Both methods overestimate the Population Growth rate.

Both methods give accurate estimates of the Population Growth Rate.

There is not enough information to tell how well either method estimates the actual Population Growth Rate.

The scatterplot shows the estimates of the Population Growth Rate (PGR) for each method along with the line y = x. However, the scatterplot does not provide any information about the actual Population Growth Rate. Therefore, it is not possible to determine how well either method estimates the actual Population Growth Rate.

Explanation

The scatterplot shows the estimates of the Population Growth Rate (PGR) for each method along with the line y = x. However, the scatterplot does not provide any information about the actual Population Growth Rate. Therefore, it is not possible to determine how well either method estimates the actual Population Growth Rate.

5. A new fertilizer is to be tested on tomato plants to determine if it increases the production of the plants. The available land is divided into eight plots. Four of the plots are on a hill and four are in a valley as shown. The plots in the valley are expected to get more water due to the influence of gravity, and those on the hill will get more direct sunlight. A randomized block design will be used, using two blocks of four plots each. Which of the following blocking schemes would be most appropriate?

Plots 1, 2, 3, and 4 in one block and plots 5, 6, 7, and 8 in the other.

Plots 1, 2, 5, and 6 in one block and plots 3, 4, 7, and 8 in the other.

Plots 1, 4, 5, and 8 in one block and plots 2, 3, 6, and 7 in the other.

Plots 1, 3, 6, and 8 in one block and plots 2, 4, 5, and 7 in the other.

The plots should be randomly assigned to blocks.

The most appropriate blocking scheme would be to have Plots 1, 2, 3, and 4 in one block and plots 5, 6, 7, and 8 in the other. This scheme ensures that the plots on the hill and in the valley are evenly distributed across the two blocks. By doing so, any potential effects of the hill or valley on the tomato plant production will be evenly spread across the blocks, allowing for a more accurate assessment of the fertilizer's impact. Randomly assigning the plots to blocks would not account for the specific conditions of the hill and valley, potentially leading to biased results.

Explanation

The most appropriate blocking scheme would be to have Plots 1, 2, 3, and 4 in one block and plots 5, 6, 7, and 8 in the other. This scheme ensures that the plots on the hill and in the valley are evenly distributed across the two blocks. By doing so, any potential effects of the hill or valley on the tomato plant production will be evenly spread across the blocks, allowing for a more accurate assessment of the fertilizer's impact. Randomly assigning the plots to blocks would not account for the specific conditions of the hill and valley, potentially leading to biased results.