A large company wants to find out what team-building activity its employees prefer. Which of the following samples can give the most valid generalization?(1 point)

Question

Responses

400 randomly chosen employees from the list of all employees
400 randomly chosen employees from the list of all employees

all 624 female employees in the company
all 624 female employees in the company

all employees who have worked in the company for 5 years or more
all employees who have worked in the company for 5 years or more

a group with one member from each department

Use the image to answer the question.

A bar graph shows pet ownership.
The x-axis shows type of pet and represents dog, cat, golfish, and hamster. The y-axis represents number of students and ranges from 0 to 11 in increments of 1. The data shows 10 dogs; 8 cats; 2 goldfish; and 3 hamsters.

Use the graph to determine the difference in the percentage of students who have dogs for pets and the percentage of students who have hamsters for pets. Round the percentages to the tenths place.

(1 point)
Responses

The difference in the percentage of students who have dogs for pets and the percentage of students who have hamsters for pets is 21.8%.
The difference in the percentage of students who have dogs for pets and the percentage of students who have hamsters for pets is 21.8%.

The difference in the percentage of students who have dogs for pets and the percentage of students who have hamsters for pets is 30.4%.
The difference in the percentage of students who have dogs for pets and the percentage of students who have hamsters for pets is 30.4%.

The difference in the percentage of students who have dogs for pets and the percentage of students who have hamsters for pets is 31%.
The difference in the percentage of students who have dogs for pets and the percentage of students who have hamsters for pets is 31%.

The difference in the percentage of students who have dogs for pets and the percentage of students who have hamsters for pets is 34.8%.
The difference in the percentage of students who have dogs for pets and the percentage of students who have hamsters for pets is 34.8%.

Use the image to answer the question.

A pie chart divided into 6 inequal sections is titled Activity Hours per Week. The sections are labeled school, 40, 24 percent; eat, 21, 13 percent; sports or play, 15, 9 percent; social media or TV, 24, 14 percent; sleep, 56; and other 12, 7 percent.

The activity for one week of 168 people was tracked and displayed in a circle graph. What was the percentage of time spent on sleep? Round the percentage to the nearest whole number.

(1 point)
The percentage of time spent on sleep was
%.

A hotel maintenance crew wants to estimate how many of the 12,000 lamps in their 30-story hotel need a new light bulb. Which of the following is a random sample of lamps to be inspected?(1 point)
Responses

all lamps from the rooms with king-sized beds
all lamps from the rooms with king-sized beds

400 lamps on the first 10 floors
400 lamps on the first 10 floors

all lamps in booked rooms
all lamps in booked rooms

100 lamps on each floor chosen randomly

A local library manager randomly surveys 80 patrons about the type of book they borrow when they visit the library. The manager finds that 3 patrons borrow novels. If the local library has 345 patrons, approximately how many of them borrow novels when they visit the library? Round your answer to the nearest whole number. (1 point)
patrons

Use the table to answer the question.

This table displays the shopping time taken by Group A and Group B for comparison.
Group A 18 20 46 34 58 31 41
Group B 15 21 32 42 29 57 39
The table shows the times, in minutes, spent shopping by two different groups. First find the mean times each group spent shopping. Then determine the difference in the mean times. Round your answers to one decimal place.(2 points)
The mean time Group A spent shopping is
minutes.
The mean time Group B spent shopping is
minutes.
The mean times Group A and Group B spent shopping differ by
minutes.

Question
Which data set has the highest median?(1 point)
Responses

{1, 6, 15, 7, 15, 18, 14}
left brace 1 comma 6 comma 15 comma 7 comma 15 comma 18 comma 14 right brace

{8, 20, 13, 14, 12, 9}
left brace 8 comma 20 comma 13 comma 14 comma 12 comma 9 right brace

{11, 15, 16, 8, 12, 14}
left brace 11 comma 15 comma 16 comma 8 comma 12 comma 14 right brace

{1, 10, 8, 29, 14, 17, 3}

Theo, Ara, Jose, and Dana all got 100 percent on their latest math test. Their scores on the previous six tests are listed. Whose mean test score will increase the most? (1 point)
Responses

Jose: 91, 93, 97, 96, 96, 96
Jose: 91, 93, 97, 96, 96, 96

Dana: 68, 74, 83, 80, 81, 82
Dana: 68, 74, 83, 80, 81, 82

Theo: 84, 88, 81, 85, 77, 76
Theo: 84, 88, 81, 85, 77, 76

Ara: 100, 98, 99, 97, 100, 100

The stem-and-leaf plot shows the speeds of the fastest steel roller coasters in Europe. The table shows the speeds of the fastest steel roller coasters in North America.

Speeds of the Fastest Steel Roller Coasters in Europe (in miles per hour)

This stem-and-leaf plot represents the speeds of the fastest steel roller coasters in Europe, where the stem indicates the tens digit and the leaf represents the ones digit.
Stem Leaf
7 4 5 5 5
8 0 0 3 4 8
9 9
11 1
Key: 7|4=74
miles per hour

Speeds of the Fastest Steel Roller Coasters in North America (in miles per hour)

This table displays the speeds of the fastest steel roller coasters in North America, categorized by country. The values represent speeds in miles per hour.
Canada 90 128 91
U.S. 93 120 100
Mexico 95 92 85
Find the range of the speeds of the fastest steel roller coasters on both continents.

(1 point)
The range of the speeds of the fastest steel roller coasters in Europe is
mph. The range of the speeds of the fastest steel roller coasters in North America is
mph.

Anthony wants to know the average daily high temperatures in his town during the summer. He chose two random samples of 10 consecutive days and recorded the daily high temperatures. The daily high temperatures in Fahrenheit are as follows.

Sample 1: 78 82 85 87 90 85 79 86 91 88
Sample 2: 81 79 80 86 89 92 82 88 84 87

Find the mean daily high temperatures of each sample and calculate the difference between these mean daily high temperatures. Express your answer as a decimal rounded to the nearest tenth.

(2 points)
The mean daily high temperature of Sample 1 is
°
.
The mean daily high temperature of Sample 2 is
°
.
The mean daily high temperatures of the two samples differ by
°
.

These are the scores for two randomly selected lacrosse teams. Find the range of the number of goals scored by each team. Based on the range, which team has a more consistent number of goals scored?

This table shows the scores of two lacrosse teams across six games.
Lacrosse Team 1: 6 0 4 17 3 12
Lacrosse Team 2: 23 14 22 14 17 22
(2 points)
The range of the number of goals scored by Lacrosse Team 1 is
. The range of the number of goals scored by Lacrosse Team 2 is
. Based on the range, Lacrosse Team
has a more consistent number of goals scored.

Use the image to answer the question.
An illustration shows two sets of dot plots. One is titled Gas Mileage in miles per gallon, Cars and the other is Gas Mileage in miles per gallon, S U Vs. The plots are shown as dots in a vertical row over each number on a number line. For Cars, a number line with arrows on both ends ranges from 18 to 22 in increments of 1. There is 1 dot above 18, 2 dots above 19, 3 dots above 20, 2 dots above 21, and 1 dot above 22. For S U Vs, a number line with arrows on both ends ranges from 21 to 25 in increments of 1. There is 1 dot above 21, 1 dot above 22, 2 dots above 23, 2 dots above 24, and 3 dots above 25.

The dot plots show the gas mileage for randomly selected cars and SUVs. Which data values do both distributions have in common?

(1 point)
The data value in common for both distributions with the lowest number is
.

The data value in common for both distributions for the highest number is
.

Question
Fifteen students are randomly selected from two different classes. They were asked how many books they read during the summer. Their responses are as follows. Find the median number of books read by each class. Which class has a higher median number of books read?

Class 1: 0, 5, 3, 6, 7, 8, 10, 1, 1, 4, 5, 6, 4, 5, 6
Class 2: 2, 2, 4, 3, 0, 0, 6, 7, 10, 9, 6, 5, 3, 1, 2

(2 points)
The median number of books read during the summer by Class 1 is
.
The median number of books read during the summer by Class 2 is
.
Class
has a higher median number of books read during the summer.

Use the image to answer the question.

Two number lines extend from 41 to 50 in increments of 1 and are labeled as Dataset A and Dataset B. The number lines show an abacus-like representation with columns of open circles over the numbers. Above the number line labeled Dataset A, there are four circles over 41, five circles over 42, seven circles over 43, four circles over 44, two circles over 45, one circle over 46, one circle over 47, three circles over 48, two circles over 49, and one circle over 50. Above the number line labeled Dataset B, there is one circle over 41, three circles over 42, three circles over 43, five circles over 44, four circles over 45, six circles over 46, seven circles over 47, four circles over 48, two circles over 49, and one circle over 50.

Two datasets of numbers from 41 to 50 are displayed in two dot plots. Compare the shapes and spreads of the dot plots. What conclusions can you draw about the shapes and the spreads?

(1 point)
Responses

Dataset A and Dataset B have equal spreads. Dataset A is skewed right, and Dataset B is symmetrical. Dataset A has a peak at 42. Dataset B has a peak at 46.
Dataset A and Dataset B have equal spreads. Dataset A is skewed right, and Dataset B is symmetrical. Dataset A has a peak at 42. Dataset B has a peak at 46.

Dataset A and Dataset B have equal spreads. Dataset A is skewed right, and Dataset B is symmetrical. Dataset A has a peak at 43. Dataset B has a peak at 47.
Dataset A and Dataset B have equal spreads. Dataset A is skewed right, and Dataset B is symmetrical. Dataset A has a peak at 43. Dataset B has a peak at 47.

Dataset A and Dataset B have equal spreads. Dataset A is skewed left, and Dataset B is symmetrical. Dataset A has a peak at 43. Dataset B has a peak at 47.
Dataset A and Dataset B have equal spreads. Dataset A is skewed left, and Dataset B is symmetrical. Dataset A has a peak at 43. Dataset B has a peak at 47.

Dataset A has a greater spread than Dataset B. Dataset A is skewed right, and Dataset B is symmetrical. Dataset A has a peak at 43. Dataset B has a peak at 47.

Maritza plays in a softball league. She wants to know about how many players in the league also play basketball. Because there are 225 players in the league, she chooses the names of 45 of the players and asks them whether they also play basketball. Describe the population and the sample. What is the size of the population, and what is the size of the sample? Show your work.(2 points)

Answer 1

Answers to Each Question:

1. Most Valid Generalization Sample

   • Answer: 400 randomly chosen employees from the list of all employees.
     This is the best sample because it includes a broad range of employees, without bias toward gender, experience, or department.

2. Difference in Pet Ownership Percentages

   • Calculation:
     • Percentage of students with dogs = \( \frac{10}{10 + 8 + 2 + 3} \times 100 = \frac{10}{23} \times 100 \approx 43.5% \)
     • Percentage of students with hamsters = \( \frac{3}{23} \times 100 \approx 13.0% \)
     • Difference = \( 43.5% - 13.0% = 30.5% \approx 30.4% \)
   • Answer: The difference in the percentage of students who have dogs for pets and the percentage of students who have hamsters for pets is 30.4%.

3. Percentage of Time Spent on Sleep

   • Data: Sleep = \(56\) hours (from the pie chart)
   • Total hours in a week = \( 168\)
   • Percentage: \( \frac{56}{168} \times 100 \approx 33.3% \) rounded to the nearest whole number is 33%.
   • Answer: The percentage of time spent on sleep was 33%.

4. Random Sample of Lamps for Inspection

   • Answer: 100 lamps on each floor chosen randomly.
     This sample is random and covers the entire hotel equally (1 lamp per floor).

5. Approximate Number of Patrons Borrowing Novels

   • Calculation: If 3 out of 80 borrow novels, then the proportion is \( \frac{3}{80} \). For 345 patrons:
     • \( 345 \times \frac{3}{80} \approx 12.9 \rightarrow 13 \) (rounded to the nearest whole number).
   • Answer: Approximately 13 patrons borrow novels.

6. Mean Shopping Times and Their Difference

   • Calculate Mean for Group A: \( \frac{18 + 20 + 46 + 34 + 58 + 31 + 41}{7} \approx \frac{254}{7} \approx 36.3 \) minutes
   • Calculate Mean for Group B: \( \frac{15 + 21 + 32 + 42 + 29 + 57 + 39}{7} \approx \frac{235}{7} \approx 33.6 \) minutes
   • Difference: \( 36.3 - 33.6 \approx 2.7 \) minutes
   • Answer: The mean time Group A spent shopping is 36.3 minutes. The mean time Group B spent shopping is 33.6 minutes. The mean times differ by 2.7 minutes.

7. Data Set with the Highest Median

   • Calculate Medians:
     • {1, 6, 15, 7, 15, 18, 14} → Ordered: {1, 6, 7, 14, 15, 15, 18} → Median is 14.
     • {8, 20, 13, 14, 12, 9} → Ordered: {8, 9, 12, 13, 14, 20} → Median is 13.
     • {11, 15, 16, 8, 12, 14} → Ordered: {8, 11, 12, 14, 15, 16} → Median is 13.
     • {1, 10, 8, 29, 14, 17, 3} → Ordered: {1, 3, 8, 10, 14, 17, 29} → Median is 10.
   • Highest Median = 14 from the first set.
   • Answer: {1, 6, 15, 7, 15, 18, 14}

8. Mean Test Score Increase

   • Scores of Jose: Mean = \( \frac{91 + 93 + 97 + 96 + 96 + 96}{6} = \frac{569}{6} \approx 94.8 \)
   • Scores of Dana: Mean = \( \frac{68 + 74 + 83 + 80 + 81 + 82}{6} = \frac{468}{6} = 78 \)
   • Scores of Theo: Mean = \( \frac{84 + 88 + 81 + 85 + 77 + 76}{6} = \frac{491}{6} \approx 81.8 \)
   • Scores of Ara: Mean = \( \frac{100 + 98 + 99 + 97 + 100 + 100}{6} = \frac{594}{6} = 99 \)
   • In terms of increase, Dana raises the lowest mean (from 78 to 100) by 22 points compared to others.
   • Answer: Dana's mean test score will increase the most.

9. Range of Roller Coaster Speeds

   • Europe: From the stem-and-leaf plot, speeds are 74, 75, 75, 75, 80, 80, 83, 84, 88, 99, 111 → Highest = 111, Lowest = 74. Range = 111 - 74 = 37 mph.
   • North America: Highest = 128, Lowest = 85. Range = 128 - 85 = 43 mph.
   • Answer: The range of the speeds in Europe is 37 mph. The range of the speeds in North America is 43 mph.

10. Mean Daily High Temperatures

    • Sample 1: \( \frac{78 + 82 + 85 + 87 + 90 + 85 + 79 + 86 + 91 + 88}{10} = \frac{870}{10} = 87 \) °.
    • Sample 2: \( \frac{81 + 79 + 80 + 86 + 89 + 92 + 82 + 88 + 84 + 87}{10} = \frac{868}{10} = 86.8 \) °.
    • Difference = \( 87 - 86.8 \approx 0.2 \) °.
    • Answer: The mean daily high temperature of Sample 1 is 87°. The mean daily high temperature of Sample 2 is 86.8°. The mean daily high temperatures differ by 0.2°.

11. Range of Goals for Lacrosse Teams

    • Team 1 Goals: 6, 0, 4, 17, 3, 12 → Lowest = 0, Highest = 17. Range = 17 - 0 = 17.
    • Team 2 Goals: 23, 14, 22, 14, 17, 22 → Lowest = 14, Highest = 23. Range = 23 - 14 = 9.
    • Answer: The range for Team 1 is 17. The range for Team 2 is 9. Team 2 has a more consistent number of goals scored (smaller range).

12. Common Data Values in Dot Plots

    • Cars: Range 18-22
    • SUVs: Range 21-25
    • Common minimum = 21, Common maximum = 22.
    • Answer: The data value in common for both distributions with the lowest number is 21. The data value in common for both distributions with the highest number is 22.

13. Median Number of Books Read

    • Class 1: Ordered {0, 1, 1, 3, 4, 5, 5, 5, 6, 6, 6, 7, 8, 10} → Median = 5.
    • Class 2: Ordered {0, 0, 0, 1, 2, 2, 3, 4, 5, 6, 6, 7, 9, 10} → Median = 3.
    • Answer: The median number of books read during the summer by Class 1 is 5. The median number of books read during the summer by Class 2 is 3. Class 1 has a higher median number of books read.

14. Analysing Dot Plots

    • Answer: Dataset A and Dataset B have equal spreads. Dataset A is skewed right, and Dataset B is symmetrical. Dataset A has a peak at 42. Dataset B has a peak at 46.

15. Population and Sample Description

    • Population: All 225 players in the league.
    • Sample: 45 players randomly chosen from the league.
    • Population Size: 225, Sample Size: 45.
    • Answer: The population size is 225 and the sample size is 45.