The data from two random samples of 200 people regarding their favorite nuts is shown in the following table.
Almond Pistachio Cashew Walnuts Total
Sample 1 40 62 63 35 200
Sample 2 43 64 61 32 200
Based on the two samples, what percentage of the people prefer cashew nuts?
a 62%
b 30.5%
c 31%
d 31.5%
The following data sets represent the highway fuel efficiency in miles per gallon (mpg) of randomly selected cars from two car companies. Which company has cars that are more consistent in highway fuel efficiency?
Car Company A: 35, 28, 35, 30, 31, 36, 35, 30
Car Company B: 29, 33, 40, 27, 34, 34, 34, 25
(1 point)
Responses
Cars from both companies have equally consistent highway fuel efficiency.
Car Company A is more consistent, because the range of highway fuel efficiency of its cars is lower than that of Car Company B.
Car Company B is more consistent, because the range of highway fuel efficiency of its cars is lower than that of Car Company A.
Car Company A is more consistent, because the range of highway fuel efficiency of its cars is higher than that of Car Company B.
Car Company A is more consistent, because the range of highway fuel efficiency of its cars is lower than that of Car Company B.
The range of Car Company A is 36 - 28 = 8 mpg, while the range of Car Company B is 40 - 25 = 15 mpg. A smaller range indicates that the data is more consistent, with values clustering around a central value. Therefore, Car Company A is more consistent in highway fuel efficiency.
The randomly selected delivery times, in minutes, of two restaurants are as follows. Which restaurant has more consistent delivery times?
Restaurant 1 Restaurant 2
40 42
37 38
40 37
41 39
38 38
46 40
41 42
37 41
40 40
(1 point)
Responses
Restaurant 2 is more consistent, because the range of its delivery times is lower than that of Restaurant 1.
The delivery times of both restaurants are equally consistent.
Restaurant 1 is more consistent, because the range of its delivery times is lower than that of Restaurant 2.
Restaurant 2 is more consistent, because the range of its delivery times is higher than that of Restaurant 1.
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The data shows the number of miles run per week by randomly selected students from two different classes. Find the difference between the medians. Which class has a higher median? By how much?
Class 1: 6, 8, 10, 11, 14, 4, 5, 8, 2, 7, 7, 5, 10, 12, 11
Class 2: 6, 4, 5, 6, 7, 8, 12, 9, 10, 11, 5, 8, 7, 4, 10
(1 point)
Responses
Class 2 has a higher median than Class 1 by 0.5 mile.
Class 1 has a higher median than Class 2 by 0.5 mile.
Class 2 has a higher median than Class 1 by 1 mile.
Class 1 has a higher median than Class 2 by 1 mile..
The median of Class 1 is:
(7 + 8) / 2 = 7.5
To find the median of Class 2, we need to put the data in order:
4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 10, 10, 11, 12
The median is the middle value, which is 8.
Therefore, Class 1 has a higher median than Class 2 by 0.5 mile.
The answer is: Class 1 has a higher median than Class 2 by 0.5 mile.
The data shows the number of seconds it took two randomly selected groups to thread a needle. Compare the measures of center and variability of these data sets.
Student Group A: 56, 14, 26, 28, 29, 45, 32, 80, 3, 10
Student Group B: 27, 24, 18, 19, 5, 16, 22, 10, 6, 20
Which of the following statements about these data sets is false?
(1 point)
Responses
The mean time taken by Group A is higher than that of Group B.
The ranges of the time taken by Group A and Group B are the same.
The amount of variability of the time taken by Group A to thread a needle is higher than the amount of variability of the time taken by Group B.
The median time taken by members of Group A to thread a needle is higher than that of members of Group B.
The median time taken by members of Group A to thread a needle is higher than that of members of Group B.
This statement is false. To compare the measures of center and variability, we can look at the mean and standard deviation of each group:
Group A: Mean = 32.3, Standard deviation = 26.1
Group B: Mean = 16.7, Standard deviation = 7.4
Therefore, the false statement is: The median time taken by members of Group A to thread a needle is higher than that of members of Group B. The median of Group A is 29 and the median of Group B is 19, so the median time taken by members of Group A is actually lower than that of members of Group B.
Two fertilizers are applied to randomly selected potato plants. After several weeks, the potatoes are weighed. The weights in kilograms are as follows. Which fertilizer is generally more effective?
Fertilizer A: 27, 20, 16, 18, 22, 19, 23, 21, 17, 19
Fertilizer B: 28, 19, 18, 21, 24, 20, 25, 27, 29, 21
(1 point)
Responses
Fertilizer B is generally more effective, because the mean and median weights of the potatoes that were treated with it are higher.
Fertilizer A is generally more effective, because the mean and median weights of the potatoes treated with it are higher.
Fertilizers A and B are equally effective, because the ranges of the weights of the potatoes are the same.
Fertilizers A and B are both ineffective, because there is no difference in the ranges of the weights of the potatoes.
Fertilizer B is generally more effective, because the mean and median weights of the potatoes that were treated with it are higher.
To compare the effectiveness of the two fertilizers, we can look at the measures of center and spread:
Fertilizer A: Mean = 19.2, Median = 19, Range = 11
Fertilizer B: Mean = 22.2, Median = 21.5, Range = 11
The mean and median weights of the potatoes treated with Fertilizer B are higher than that of Fertilizer A, indicating that it was generally a more effective fertilizer. The ranges of both fertilizers are the same, so they are not a deciding factor in determining effectiveness.
Therefore, the correct answer is: Fertilizer B is generally more effective, because the mean and median weights of the potatoes that were treated with it are higher.
b 30.5%
To find the percentage of people who prefer cashew nuts, we need to add up the number of people who chose cashews in both samples and divide by the total number of people.
In Sample 1, 63 people chose cashews.
In Sample 2, 61 people chose cashews.
Total number of people = 200 + 200 = 400
Therefore, the percentage of people who prefer cashews is:
(63 + 61) / 400 = 0.305 or 30.5%