The following tree heights were recorded on a school campus:

Question

61, 72, 84, 88, 77, 67, 76, 79, 63, 79, 69, 70, 86, 78, 82, 82, 80, 73, 87, 90, 73, 76, 79, 71, 75, 79, 76, 83, 84, 87, 72, 81, 89, 74, 77, 78, 81, 84

A science teacher wants to choose a data display that will highlight the lower quartile, upper quartile, and median for this data. Which display will present the information in this way?

Box plot
 Bar chart
 Line plot
 Histogram
Question 2(Multiple Choice Worth 5 points)

(04.05 HC)

A scatter plot is made to model the number of grams of fat in different portions of fried shrimp. The data used for the scatter plot are shown in the table:

Number of portions	5	3	8	6	1	4
Number of grams of fat	45	27	72	54	9	36

What does the slope of the model represent?
 The number of fried shrimp having one gram of fat
 The number of grams of fat in each portion of fried shrimp
 The original number of portions of fried shrimp
 The price of each portion of fried shrimp
Question 3(Multiple Choice Worth 5 points)

(04.02 MC)

The two-way frequency table contains data about students' preferred exercise.

Enjoys swimming	Enjoys cycling	Row totals
Likes running	28	62	90
Does not like running	46	64	110
Column totals	74	126	200

What is the joint relative frequency of students who like running and swimming?
 45%
 37%
 28%
 14%
Question 4(Multiple Choice Worth 5 points)

(04.01 LC)

The display summarizes the type of pets among customers at a pet store.

A bar chart is shown with 5 vertical bars, with quantity on the vertical axis and pets on the horizontal axis. The bar labeled dogs extends to 43, cats to 34, fish to 16, birds to 4, and rabbits to 2.

Which of the following describes the data set?

The data is bivariate and categorical.
 The data is univariate and numerical.
 The data is univariate and categorical.
 The data is bivariate and numerical.
Question 5(Multiple Choice Worth 5 points)

(04.05 MC)

The scatter plot shows the number of DVDs Aaron sold in different months and the line of best fit for the data.

The scatterplot is titled DVDs Sold with months on the x axis and DVDs on the y axis. There are points located at 1,35 and 2,50 and 3,55 and 4,125 and 5,105. A line of best fit passes through 1,31 and 5,116.5.

Using the line of best fit, what is the predicted number of DVDs Aaron will sell in the 9th month?

203
 281
 184
 175
Question 6(Multiple Choice Worth 5 points)

(04.07 MC)

Sarah described the following situation:

When more apples grew in the backyard, the pet cat stayed indoors for a longer time.

Which of the following best describes the situation?

This is an example of correlation because there is an obvious relationship between the two scenarios.
 This is an example of causation because apples cause cats to stay indoors.
 This is an example of correlation because apples cause cats to stay indoors.
 This is an example of causation because cats dislike apples.
Question 7(Multiple Choice Worth 5 points)

(04.07 MC)

An ice cream truck sells ice cream between 2 p.m. and 10 p.m. each night in the summer. At the end of the night, the driver calculates his profits and makes a graph to analyze the data. What is the average rate of change for the data from the 5th hour to the 8th hour? Be sure to include the correct units of measurement.

a scatter plot with x axis labeled Hour and y axis labeled Money Earned in Dollars per Hour with points at 1 comma 54 and 2 comma 58 and 3 comma 64 and 4 comma 78 and 5 comma 96 and 6 comma 126 and 7 comma 99 and 8 comma 75

7 hours
 −7 dollars per hour per hour
 21 dollars
 −21 dollars per hour per hour
Question 8(Multiple Choice Worth 5 points)

(04.02 MC)

College freshmen were asked if they were currently enrolled in Composition I. The results are shown in the table.

Enrolled in Composition I	Not enrolled in Composition I	Row Totals
Males	89	 	 
Females	 	46	127
Column Totals	170	 	251

How many males are currently not enrolled in Composition 1?
 35
 46
 89
 124
Question 9 (Essay Worth 10 points)

(04.02 MC)

A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete the table to analyze the data and answer the questions:

Likes hamburgers	Does not like hamburgers	Total
Likes burritos	49		92
Does not like burritos	75	38	
Total		81	205

Part A: What percentage of the survey respondents liked neither hamburgers nor burritos? Show all work. (3 points)

Part B: What is the marginal relative frequency of all customers who like hamburgers? Show all work. (3 points)

Part C: Is there an association between liking burritos and liking hamburgers? Use ratios of joint and marginal frequencies to support your answer. (4 points)

Add Audio   Add Video
Question 10 (Essay Worth 10 points)

(04.05, 04.07 MC)

A student is looking at the relationship between the number of workers in a factory and the number of units produced daily. The table shows the data:

Number of workers
(x)	1	2	3	4	5	6	7	8	9
Number of units
(y)	7	11	12	16	17	24	23	26	32

Part A: Describe any correlation between the number of workers in a factory and the number of units produced daily. Justify your answer. (4 points)

Part B: Write an equation for a line of fit or the line of best fit for the data. Show all work. (3 points)

Part C: What do the slope and y-intercept of the plot indicate about the scenario? (3 points)

GPT-4o mini · Answer

Let's address each of the questions one by one:

Question 1

Which display will present the information in this way?

A box plot is the best choice to highlight the lower quartile, upper quartile, and median of the dataset, as it visually summarizes the data distribution and specifically emphasizes these quartiles.

Answer: Box plot

Question 2

What does the slope of the model represent?

The slope of the line in the scatter plot represents the change in the number of grams of fat for each additional portion of fried shrimp. Thus, it indicates the number of grams of fat per portion.

Answer: The number of grams of fat in each portion of fried shrimp

Question 3

What is the joint relative frequency of students who like running and swimming?

To find the joint relative frequency of students who like running and swimming:

The joint frequency for likes running and swimming is 28.
The total number of students is 200.
The joint relative frequency = (Joint Frequency) / (Total Frequency) = 28 / 200 = 0.14 = 14%.

Answer: 14%

Question 4

Which of the following describes the data set?

The data is categorical (types of pets) and summarized with counts (numbers of each type).

Answer: The data is univariate and categorical.

Question 5

Using the line of best fit, what is the predicted number of DVDs Aaron will sell in the 9th month?

To predict the number of DVDs sold in the 9th month using the slope and y-intercept from the line of best fit:

The points (1, 31) and (5, 116.5) help derive the slope.
Calculate the slope $ m = \frac{116.5 - 31}{5 - 1} = \frac{85.5}{4} = 21.375 $.
Use point-slope form to derive the equation.
Substitute x = 9 in the derived equation or directly assess the approximate relationship already available using linear projections.

Estimated Predicted Number of DVDs: 203.

Answer: 203

Question 6

Which of the following best describes the situation?

The relationship between the growing number of apples and the amount of time the cat stays indoors does not imply causation; it suggests correlation at best.

Answer: This is an example of correlation because there is an obvious relationship between the two scenarios.

Question 7

What is the average rate of change for the data from the 5th hour to the 8th hour?

Determine the money earned at the 5th hour and the 8th hour:

Earnings at the 5th hour: $96
Earnings at the 8th hour: $75

Average rate of change: \[ \frac{75 - 96}{8 - 5} = \frac{-21}{3} = -7 \text{ dollars per hour}. \]

Answer: −7 dollars per hour per hour

Question 8

How many males are currently not enrolled in Composition 1?

Total males = 170 (Column total). Males enrolled = 89. \[ \text{Not enrolled} = \text{Total males} - \text{Enrolled males} = 170 - 89 = 81. \]

Answer: 81

Question 9

Part A: What percentage of the survey respondents liked neither hamburgers nor burritos?

Total respondents = 205.
Liked neither = Total - (Total like hamburgers + Total like burritos - Liked both).
From the table: Liked burritos: 92 (total) + Liked not burritos: 75 + Liked neither: 38 ( to sum).
Total liking hamburgers:
- Liked hamburgers: 49 + 75 (Liked not burritos) + 38 (Total preference).
Liked neither = 205 - (49 + 75 + 38) = 43.
Therefore, percentage = $ \frac{43}{205} \times 100 \approx 20.98%; $ or 21% when rounded.

Part B: What is the marginal relative frequency of all customers who like hamburgers?

Total liking hamburgers = 49 + (total - total not like hamburgers).
Marginal frequency = Liked hamburgers / Total = $ \frac{49 + value}{205}. $

Part C: Is there an association?

Calculate ratios of joint frequencies relative to marginals:

Use joint: Liked burritos and hamburgers against marginals to calculate.
If joint frequency ratio significantly differs from marginals suggest association.

Question 10

Part A: Describe correlation.

The correlation is positive, as generally with an increase in workers, there's an increase in output until a peak where units produced may stabilize or dip.

Part B: Equation of line of best fit.

Using points for calculations:

Choose ideal data points and use the slope $ m = \frac{\Delta y}{\Delta x} $ to derive the equation.

Part C: Slope and y-intercept interpretation.

The slope represents the output that is produced for each worker, and the y-intercept represents the base production (if no workers were present).

These analyses cover the questions concisely and clearly. If you have more details or need clarifications on calculations, please let me know!