B. This sample includes only those students who use the library.
D. This sample is not a random sample.
Seth wants to find out if students at Hillsboro High School go to the football games. He decides to take a sample rather than ask every student. He asks the first 15 boys leaving the library. Which statement about the sample is true? Select two answers.
A.
This sample includes the entire student population.
B.
This sample includes only those students who use the library.
C.
This sample is representative of the population.
D.
This sample is not a random sample.
E.
This sample is a random sample.
11 answers
Which of the following is true of a random sample?
A. It is the only way to sample a population.
B. Each member of the sample is a volunteer.
C. It is always the easiest way to sample a population.
D. Each member of the population has an equal chance of being selected.
A. It is the only way to sample a population.
B. Each member of the sample is a volunteer.
C. It is always the easiest way to sample a population.
D. Each member of the population has an equal chance of being selected.
D. Each member of the population has an equal chance of being selected.
Note: Your teacher will grade your response to questions 7–8 to ensure you receive proper credit for your answer.
There are 3,000 people at a concert. You survey a random sample of 200 people and find that for 35 of them this is the first concert they have ever attended. Estimate how many total people are attending their first concert that night.
There are 3,000 people at a concert. You survey a random sample of 200 people and find that for 35 of them this is the first concert they have ever attended. Estimate how many total people are attending their first concert that night.
To estimate the total number of people attending their first concert, we can use the formula:
(total number of people in population) = (number of people in sample) x (number of people in sample who meet the criteria) / (number of people in sample who were asked about the criteria)
Plugging in the given values, we get:
(total number of people in population) = (3,000) x (35) / (200) = 525
Therefore, we can estimate that about 525 people in the total population are attending their first concert that night.
(total number of people in population) = (number of people in sample) x (number of people in sample who meet the criteria) / (number of people in sample who were asked about the criteria)
Plugging in the given values, we get:
(total number of people in population) = (3,000) x (35) / (200) = 525
Therefore, we can estimate that about 525 people in the total population are attending their first concert that night.
You want to conduct a survey to find out what sport the students at your school prefer to play.
a) You interview 20 boys playing football at lunch. Is this a random sample? Explain.
b) The survey question you ask is, “What is your favorite sport to play?” Is the question fair or biased? Explain.
a) You interview 20 boys playing football at lunch. Is this a random sample? Explain.
b) The survey question you ask is, “What is your favorite sport to play?” Is the question fair or biased? Explain.
a) No, this is not a random sample because the sample was not selected randomly from the entire population of students at the school. The sample only includes boys who are playing football at lunch, which means that only those interested in playing football were surveyed. This may not be representative of the entire student population.
b) The question appears to be fair because it is asking for the students' personal preference for a sport to play, which is subjective to each individual. However, there is a potential issue of bias if the question is only asked to students who are already actively involved in sports, as this could lead to a sample that is not representative of the entire student population. Additionally, the question only allows for responses about sports that the students prefer to play, which may exclude sports that students may enjoy watching or following but do not play themselves.
b) The question appears to be fair because it is asking for the students' personal preference for a sport to play, which is subjective to each individual. However, there is a potential issue of bias if the question is only asked to students who are already actively involved in sports, as this could lead to a sample that is not representative of the entire student population. Additionally, the question only allows for responses about sports that the students prefer to play, which may exclude sports that students may enjoy watching or following but do not play themselves.
ote: Your teacher will grade your response to questions 7–8 ensure that you receive proper credit for your answer.
The graph below shows the number of new clients brought into Sunnydays Insurance Company. Why is the graph misleading?
A line graph is shown.
The horizontal axis of the graph is labeled Year. The hash marks are equally spaced. Every other hash mark is labeled, starting at the left with the first hash mark as 1990, then the third has mark as 1991, fifth hash mark as 1993, seventh hash mark as 1997, and the ninth hash mark as 2003.
The vertical axis of the graph is labeled New Clients. The hash marks are equally spaced. Every other hash mark is labeled from the bottom to the top. The second hash mark is 100. The fourth hash mark is 200. The sixth hash mark is 300.
Five points are connected by line segments in order from left to right.
The first point is at 1990 comma 50.
The second point is at 1991 comma 100.
The third point is at 1993 comma 150.
The fourth point is at 1997 comma 200.
The fifth point is at 2003 comma 250.
The graph below shows the number of new clients brought into Sunnydays Insurance Company. Why is the graph misleading?
A line graph is shown.
The horizontal axis of the graph is labeled Year. The hash marks are equally spaced. Every other hash mark is labeled, starting at the left with the first hash mark as 1990, then the third has mark as 1991, fifth hash mark as 1993, seventh hash mark as 1997, and the ninth hash mark as 2003.
The vertical axis of the graph is labeled New Clients. The hash marks are equally spaced. Every other hash mark is labeled from the bottom to the top. The second hash mark is 100. The fourth hash mark is 200. The sixth hash mark is 300.
Five points are connected by line segments in order from left to right.
The first point is at 1990 comma 50.
The second point is at 1991 comma 100.
The third point is at 1993 comma 150.
The fourth point is at 1997 comma 200.
The fifth point is at 2003 comma 250.
Without a specific scale on the vertical axis, it is difficult to determine the actual values for the number of new clients. The viewer is left to estimate the values based on the position of the hash marks, which can be misleading. Additionally, the vertical axis only goes up to 300, which may give the impression that the growth in new clients is less significant than it actually is. Finally, the graph only shows five data points over the course of 13 years, which may not provide a complete picture of the trends and fluctuations in new clients over time.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Rolinda’s first five Spanish test scores are 85, 85, 60, 62, and 59.
a. Find the mean, the median, and the mode of Rolinda’s Spanish test scores. Round your answers to the nearest tenth, if necessary.
b. Which of these measures best supports Rolinda’s claim that she is doing well in her Spanish class?
c. Why is Rolinda’s claim misleading?
Rolinda’s first five Spanish test scores are 85, 85, 60, 62, and 59.
a. Find the mean, the median, and the mode of Rolinda’s Spanish test scores. Round your answers to the nearest tenth, if necessary.
b. Which of these measures best supports Rolinda’s claim that she is doing well in her Spanish class?
c. Why is Rolinda’s claim misleading?
a. To find the mean, we add up all of Rolinda's scores and divide by the total number of scores:
Mean = (85 + 85 + 60 + 62 + 59) / 5 = 70.2 (rounded to the nearest tenth)
To find the median, we need to arrange the scores in order from smallest to largest:
59, 60, 62, 85, 85
The middle number is 62, so the median is 62.
To find the mode, we look for the score that appears most frequently. In this case, both 85 and 60 appear twice, while 59 and 62 each appear once. Therefore, there is no mode for this set of scores.
b. The measure that best supports Rolinda's claim that she is doing well in her Spanish class is the mean, since it takes into account all of her scores and gives an average value. With a mean score of 70.2, it appears that she is doing reasonably well overall.
c. Rolinda's claim is misleading because the mean score of 70.2 is not a representative measure of her performance on individual tests. Her scores show a wide range of performance, with two scores of 85 and three scores below 63. This suggests that she may be struggling with certain concepts and areas of the curriculum, even though her overall mean score may appear to be decent. Additionally, the lack of a mode indicates that there is no single score that is most representative of her performance, suggesting inconsistency and variability in her results.
Mean = (85 + 85 + 60 + 62 + 59) / 5 = 70.2 (rounded to the nearest tenth)
To find the median, we need to arrange the scores in order from smallest to largest:
59, 60, 62, 85, 85
The middle number is 62, so the median is 62.
To find the mode, we look for the score that appears most frequently. In this case, both 85 and 60 appear twice, while 59 and 62 each appear once. Therefore, there is no mode for this set of scores.
b. The measure that best supports Rolinda's claim that she is doing well in her Spanish class is the mean, since it takes into account all of her scores and gives an average value. With a mean score of 70.2, it appears that she is doing reasonably well overall.
c. Rolinda's claim is misleading because the mean score of 70.2 is not a representative measure of her performance on individual tests. Her scores show a wide range of performance, with two scores of 85 and three scores below 63. This suggests that she may be struggling with certain concepts and areas of the curriculum, even though her overall mean score may appear to be decent. Additionally, the lack of a mode indicates that there is no single score that is most representative of her performance, suggesting inconsistency and variability in her results.
1 answer