Statistics unit test
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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?
The sample that can give the most valid generalization is the one that includes a representative mix of the company's employees who are likely to participate in team-building activities.
One possible approach to sampling is to randomly select a proportionate number of employees from each department or division, ensuring that each team is represented. This would provide a diverse and representative sample of employees who can accurately reflect the preferences of the broader employee population.
Another approach would be to conduct a survey among all employees and ensure that the response rate is high enough to ensure a representative sample. This would provide a comprehensive view of the preferences of all employees, making it possible to make valid generalizations about employee preferences.
In summary, the sample that includes a diverse and representative mix of employees who are likely to participate in team-building activities would give the most valid generalization.
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)
Responses
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
400 randomly chosen employees from the list of all employees
400 randomly chosen employees from the list of all employees
a group with one member from each department
a group with one member from each department
all 624 female employees in the company
all 624 female employees in the company
The sample that can give the most valid generalization is 400 randomly chosen employees from the list of all employees. This is because the sample is randomly selected from the entire employee population and is likely to be representative of the broader employee population. Additionally, the sample size of 400 is large enough to potentially provide reliable and accurate data on employee preferences.
The other samples do not necessarily provide a representative or diverse enough mix of employees to accurately reflect the preferences of the broader employee population. For example, limiting the sample to employees who have worked in the company for 5 years or more or only including female employees would result in biased and non-representative samples. Similarly, a group with one member from each department may not accurately reflect the preferences of employees who are likely to participate in team-building activities.
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
400 lamps on the first 10 floors
all lamps from the rooms with king-sized beds
all lamps in booked rooms
100 lamps on each floor chosen randomly
A random sample of lamps to be inspected would be 100 lamps on each floor chosen randomly. This is because a random sample is chosen in such a way that every lamp has an equal chance of being selected and there is no bias in the sampling method. Selecting a fixed number of lamps on each floor (such as in option A) may result in bias if there are differences in the distribution of lamps needing replacement across floors. Similarly, selecting all lamps in certain types of rooms (such as in option B or C) may not provide a representative sample. Therefore, the best option is to randomly select a fixed number of lamps on each floor.
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.
To estimate the number of patrons who borrow novels when they visit the library, we can use the proportion of patrons who borrowed novels in the sample (3/80) and apply it to the total number of patrons in the library (345):
Proportion of patrons in the sample who borrowed novels = 3/80
Total number of patrons in the library = 345
Estimated number of patrons who borrow novels = Proportion of patrons who borrow novels x Total number of patrons in the library
Estimated number of patrons who borrow novels = (3/80) x 345
Estimated number of patrons who borrow novels = 12.94
Rounding this to the nearest whole number, the estimated number of patrons who borrow novels when they visit the library is 13.
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)
To find the mean time spent shopping for Group A, we can add up all the values and divide by the total number of values:
Mean time for Group A = (18 + 20 + 46 + 34 + 58 + 31 + 41) / 7
Mean time for Group A = 31.4 minutes
To find the mean time spent shopping for Group B, we can follow the same process:
Mean time for Group B = (15 + 21 + 32 + 42 + 29 + 57 + 39) / 7
Mean time for Group B = 33.4 minutes
The difference in mean times between the two groups can be found by subtracting the mean time for Group A from the mean time for Group B:
Difference in mean times = Mean time for Group B - Mean time for Group A
Difference in mean times = 33.4 - 31.4
Difference in mean times = 2.0 minutes
Rounding this to one decimal place, the difference in mean times is 2.0 minutes.
Which data set has the highest median?(1 point)
Responses:
{11, 15, 16, 8, 12, 14}
{1, 6, 15, 7, 15, 18, 14}
{1, 10, 8, 29, 14, 17, 3}
{8, 20, 13, 14, 12, 9}
To find the median of each data set, we need to arrange the values in order from lowest to highest and then find the middle value or average of the middle two values if there are an even number of values.
For the given data sets:
- {11, 15, 16, 8, 12, 14} has a median of 13.5
- {1, 6, 15, 7, 15, 18, 14} has a median of 15
- {1, 10, 8, 29, 14, 17, 3} has a median of 10
- {8, 20, 13, 14, 12, 9} has a median of 13.5
Therefore, data set {1, 6, 15, 7, 15, 18, 14} has the highest median of 15.
Value per House Number of Houses
$150,000 2
$220,000 4
$490,000 3
$540,000 2
$800,000 5
$975,000 2The values of several houses on Mango Street are displayed on the table. What is the median value of these houses?
To find the median value of the houses, we need to arrange the values from lowest to highest:
$150,000, $220,000, $490,000, $540,000, $800,000, $800,000, $800,000, $800,000, $800,000, $975,000, $975,000
There are 11 values in the data set, so the median is the middle value.
The median is $800,000 because it is the value that lies in the middle after arranging the values in order.
Therefore, the median value of the houses on Mango Street is $800,000.
Number of Houses 2, 4, 3, 2, 5, 2 and they all match up with the prices from descending order.
Value per house: $150,000
$220,000
$490,000
$540,000
$800,000
$975,000 The values of several houses on Mango Street are displayed on the table. What is the median value of these houses?
To find the median value of the houses, we need to use the values given in descending order:
$975,000, $800,000, $800,000, $800,000, $800,000, $540,000, $490,000, $220,000, $150,000
There are 18 values in total, which is an even number. To find the median, we need to take the average of the two middle values, which are the ninth and tenth values:
Median = ($490,000 + $540,000) / 2 = $515,000
Therefore, the median value of the houses on Mango Street is $515,000.
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
Dana: 68, 74, 83, 80, 81, 82
Dana: 68, 74, 83, 80, 81, 82
Jose: 91, 93, 97, 96, 96, 96
Jose: 91, 93, 97, 96, 96, 96
Theo: 84, 88, 81, 85, 77, 76
Theo: 84, 88, 81, 85, 77, 76
Ara: 100, 98, 99, 97, 100, 100
To determine whose mean test score will increase the most, we need to calculate the mean of each student's previous six test scores and then compare them to the perfect score of 100 on the latest test:
- Dana: Mean test score = (68 + 74 + 83 + 80 + 81 + 82) / 6 = 78
- Jose: Mean test score = (91 + 93 + 97 + 96 + 96 + 96) / 6 = 95
- Theo: Mean test score = (84 + 88 + 81 + 85 + 77 + 76) / 6 = 82
- Ara: Mean test score = (100 + 98 + 99 + 97 + 100 + 100) / 6 = 99
From these calculations, we can see that Ara has the highest mean test score of 99, and the perfect score on the latest test will not have any impact on her mean score.
The student whose mean score will increase the most is Dana, who had a mean score of 78 before the latest test and now has a perfect score of 100. This raises her mean score by 22/7 ≈ 3.14, which is the largest increase out of all the students.
Therefore, Dana's mean test score will increase the most among the four students.
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
Dana: 68, 74, 83, 80, 81, 82
Jose: 91, 93, 97, 96, 96, 96
Theo: 84, 88, 81, 85, 77, 76
Ara: 100, 98, 99, 97, 100, 100
To determine whose mean test score will increase the most, we need to calculate the mean of each student's previous six test scores and then compare them to the perfect score of 100 on the latest test:
- Dana: Mean test score = (68 + 74 + 83 + 80 + 81 + 82) / 6 = 78
- Jose: Mean test score = (91 + 93 + 97 + 96 + 96 + 96) / 6 = 95
- Theo: Mean test score = (84 + 88 + 81 + 85 + 77 + 76) / 6 = 82
- Ara: Mean test score = (100 + 98 + 99 + 97 + 100 + 100) / 6 = 99
From these calculations, we can see that Ara has the highest mean test score of 99, and the perfect score on the latest test will not have any impact on her mean score.
The student whose mean score will increase the most is Dana, who had a mean score of 78 before the latest test and now has a perfect score of 100. This raises her mean score by 22/7 ≈ 3.14, which is the largest increase out of all the students.
Therefore, Dana's mean test score will increase the most among the four students.
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)
Stem Leaf
7 4 5 5 5
8 0 0 3 4 8
9 9
11 1Key: 7|4=74 miles per hour
Speeds of the Fastest Steel Roller Coasters in North America (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)
To find the range of the speeds of the fastest steel roller coasters in both Europe and North America, we need to first determine the lowest and highest speeds in each region.
For Europe, the lowest speed is 74 mph and the highest speed is 111 mph (which is represented by the stem 11 and leaf 1 in the stem-and-leaf plot).
For North America, the lowest speed is 85 mph and the highest speed is 128 mph (as listed in the table).
Therefore, the range of the speeds of the fastest steel roller coasters in Europe and North America are:
- Europe: 111 - 74 = 37 mph
- North America: 128 - 85 = 43 mph
So the range of the speeds for the fastest steel roller coasters is higher in North America than in Europe.
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.
(2 points)
To find the mean daily high temperatures of each sample, we need to add up all the daily high temperatures in each sample and divide by the number of temperatures in the sample:
Sample 1 mean = (78 + 82 + 85 + 87 + 90 + 85 + 79 + 86 + 91 + 88) / 10 = 85.1°F
Sample 2 mean = (81 + 79 + 80 + 86 + 89 + 92 + 82 + 88 + 84 + 87) / 10 = 85.8°F
To find the difference between the mean daily high temperatures, we subtract the mean of Sample 1 from the mean of Sample 2:
Sample 2 mean - Sample 1 mean = 85.8 - 85.1 = 0.7°F
Therefore, the difference between the mean daily high temperatures of the two samples is 0.7°F.
The data from two random samples of 100 students regarding what pet they own is given below.
Dog Cat Bird Total
Sample 1: 54 38 8 100
Sample 2: 39 49 12 100
Based on the two samples, what percentage of students own a bird as a pet?
(1 point)
To find the percentage of students who own a bird as a pet based on the two samples, we need to add up the number of students who own a bird in each sample and then divide by the total number of students in both samples:
Total number of students who own a bird = 8 + 12 = 20
Total number of students in both samples = 100 + 100 = 200
Percentage of students who own a bird = (Total number of students who own a bird / Total number of students in both samples) x 100
Percentage of students who own a bird = (20 / 200) x 100
Percentage of students who own a bird = 10%
Therefore, based on the two samples, 10% of students own a bird as a pet.
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?
Lacrosse Team 1: 6 0 4 17 3 12
Lacrosse Team 2: 23 14 22 14 17 22(2 points)
To find the range of the number of goals scored by each lacrosse team, we need to subtract the lowest score in each team from the highest score in each team:
- Range for Lacrosse Team 1: 17 - 0 = 17
- Range for Lacrosse Team 2: 23 - 14 =
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?
Lacrosse Team 1: 6, 0, 4, 17, 3, 12
Lacrosse Team 2: 23, 14, 22, 14, 17, 22
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?
Lacrosse Team 1: 6 0 4 17 3 12
Lacrosse Team 2: 23 14 22 14 17 22
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?
Lacrosse Team 1: 6 0 4 17 3 12
Lacrosse Team 2: 23 14 22 14 17 22
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.
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)