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?
a group with one member from each department
400 randomly chosen employees from the list of all employees
all 624 female employees in the company
all employees who have worked in the company for 5 years or more
Option B: 400 randomly chosen employees from the list of all employees.
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
Find the median of books read in the summer by class 1:
Find the median of books read in the summer by class 2:
To find the median, we need to order the values from least to greatest and find the middle value. If there is an even number of values, we take the mean of the middle two values.
For Class 1:
0, 1, 1, 3, 4, 4, 5, 5, 5, 6, 6, 7, 8, 10
There are 14 values, so we take the mean of the 7th and 8th values: (5+5)/2 = 5
For Class 2:
0, 0, 1, 2, 2, 2, 3, 3, 4, 5, 6, 6, 7, 9, 10
There are 15 values, so the median is the 8th value: 3
Therefore, Class 1 has a higher median number of books read during the summer (5) than Class 2 (3).
The ages of randomly selected employees at two companies are recorded. Their ages are as follows.
Company A: 34, 28, 36, 27, 45, 44, 30, 42, 41, 40, 50, 48, 52, 45, 39, 38
Company B: 29, 32, 48, 51, 49, 37, 33, 35, 36, 40, 45, 48, 43, 43, 44, 48
Which of the following statements is true?
The mean age of employees from Company A is higher than the mean age of employees from Company B.
The median age of employees from Company A is lower than the median age of employees from Company B.
The range of ages of employees from Company A is higher than the range of ages of employees from Company B.
The mean is found by adding up all the ages and dividing by the total number of employees. The median is the middle age when all the ages are ordered from least to greatest. The range is the difference between the highest and lowest age.
For Company A:
Mean: (34+28+36+27+45+44+30+42+41+40+50+48+52+45+39+38)/16 = 40.75
Median: 41
Range: 52-27 = 25
For Company B:
Mean: (29+32+48+51+49+37+33+35+36+40+45+48+43+43+44+48)/16 = 41.125
Median: 43.5
Range: 51-29 = 22
Therefore, statement 1 is false because the mean age of Company A is 40.75 which is lower than the mean age of Company B, which is 41.125. Statement 2 is false because the median age of Company A is 41, which is higher than the median age of Company B, which is 43.5. Statement 3 is false because the range of ages of Company A is 25, which is lower than the range of ages of Company B, which is 22.
pick 2 statements
The mean age of employees from Company B is higher than the mean age of employees from Company A.
The median age of employees from Company A is lower than the median age of employees from Company B.
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)
The population is all the players in the softball league, and the sample is the 45 players that Maritza chose and surveyed.
The size of the population is 225, as stated in the problem.
The size of the sample is 45, as Maritza surveyed 45 players.
The most valid generalization can be obtained by using a representative sample that accurately reflects the characteristics of the entire employee population. In this case, we want to find out what team-building activity the employees prefer, so we need a sample that includes a diverse range of employees from different departments and backgrounds.
Option a: A group with one member from each department may be representative in terms of capturing different departments, but it does not guarantee diversity in other factors such as years of experience, gender, or other relevant characteristics.
Option b: Choosing 400 randomly chosen employees from the list of all employees is a good approach as it ensures a random and diverse selection from the entire population. This sample could provide a valid generalization if the company has a large number of employees and the sample is an accurate representation of the overall population.
Option c: Selecting all 624 female employees in the company may be useful if the team-building activity has a specific focus on gender-related factors. However, it would not be representative of the entire employee population and would provide limited insights.
Option d: Considering all employees who have worked in the company for 5 years or more may capture some level of experience and commitment, but it may exclude newer employees who have valuable input. It may not be representative if the company has a high turnover rate or has many employees with less than 5 years of experience.
Based on these considerations, option b (400 randomly chosen employees from the list of all employees) is likely to provide the most valid generalization as it provides a balanced representation of the entire employee population.