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SAT Practice Test 2015. A sociologist chose 300 students at random from each of two schools and asked each student how many siblings he or she has. The results are shown in the table below.
There are a total of 2,400 students at Lincoln School and 3,300 students at Washington School.
What is the median number of siblings for all the students surveyed?
A) 0
B) 1
C) 2
D) 3
The "median" is the value positioned in the middle of a list of values.
There are a total of 600 students in the survey:
260 students with 0 siblings (position 1 to 260 in the list)
190 students with 1 siblings (position 261 to 450 in the list)
90 students with 2 siblings (position 451 to 540 in the list)
40 students with 3 siblings (position 541 to 580 in the list)
20 students with 4 siblings (position 581 to 600 in the list)
The median will be the value in the position 300 or 301 in the list, that is, a student with 1 sibling.
Answer: B
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SAT Practice Test 2015. The following question refers to the data in the previous question:
Based on the survey data, which of the following most accurately compares the expected total number of students with 4 siblings at the two schools?
A) The total number of students with 4 siblings is expected to be equal at the two schools.
B) The total number of students with 4 siblings at Lincoln School is expected to be 30 more than at Washington School.
C) The total number of students with 4 siblings at Washington School is expected to be 30 more than at Lincoln School.
D) The total number of students with 4 siblings at Washington School is expected to be 900 more than at Lincoln School.
There are 300 students surveyed in Lincoln School, 10 of which have 4 siblings. Since there are a total of 2,400 students in Lincoln School, its expected total number of students with 4 siblings is:
(10/300)(2,400)=80 students.
There are 300 students surveyed in Washington School, 10 of which have 4 siblings. Since there are a total of 3,300 students in Washington School, its expected total number of students with 4 siblings is:
(10/300)(3,300)=110 students.
Answer: C
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SAT Practice Test 2015. A survey was taken of the value of homes in a county, and it was found that the mean home value was 165,000 dollars and the median home value was 125,000 dollars. Which of the following situations could explain the difference between the mean and median home values in the county?
A) The homes have values that are close to each other.
B) There are a few homes that are valued much less than the rest.
C) There are a few homes that are valued much more than the rest.
D) Many of the homes have values between 125,000 and 165,000 dollars.
The "mean" is the average, calculated by adding up all the values and dividing by the number of values.
The "median" is the value positioned in the middle of a list of values.
Whenever there are outliers in the data, the mean will be pulled in their direction while the median remains the same. The example in the question has a mean that is larger than the median, and so one possible explanation is that there are a few homes that are valued much more than the rest..
Answer: C
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SAT Practice Test 2015.
The table above summarizes the results of 200 law school graduates who took the bar exam. If one of the surveyed graduates who passed the bar exam is chosen at random for an interview, what is the probability that the person chosen did not take the review course?
A) 18/25
B) 7/25
C) 25/200
D) 7/200
Answer:A) 18/25
B) 7/25
C) 25/200
D) 7/200
There are a total of 25 graduates who passed the bar exam (18 who took the review course, 7 who did not take the review course). Thus the probability that the person chosen did not take the review course is 7/25.
Answer: B
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SAT Practice Test 2015. A researcher conducted a survey to determine whether people in a certain large town prefer watching sports on television to attending the sporting event. The researcher asked 117 people who visited a local restaurant on a Saturday, and 7 people refused to respond. Which of the following factors makes it least likely that a reliable conclusion can be drawn about the sports-watching preferences of all people in the town?
A) Sample size
B) Population size
C) The number of people who refused to respond
D) Where the survey was given
The results of the survey will be reliable only if the participants have been randomly selected from ALL people in that population. The fact that the research was conducted only with people who visited a local restaurant makes it least likely that a reliable conclusion can be drawn about the sports-watching preferences of all people in the town.
Answer: D
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SAT 2015 Test. A square field measures 10 meters by 10 meters. Ten students each mark off a randomly selected region of the field; each region is square and has side lengths of 1 meter, and no two regions overlap. The students count the earthworms contained in the soil to a depth of 5 centimeters beneath the ground’s surface in each region. The results are shown in the table below.
Which of the following is a reasonable approximation of the number of earthworms to a depth of 5 centimeters beneath the ground’s surface in the entire field?
A) 150
B) 1,500
C) 15,000
D) 150,000
Answer:
Since the field is 10 meters by 10 meters, its total area is 100m².
The lowest number of earthworms found in 1m² is 107. In 100m² there would be 10,700 earthworms.
The largest number of earthworms found in 1m² is 176. In 100m² there would be 17,600 earthworms.
Therefore the answer should be between 10,700 and 17,600 earthworms.
Answer: C
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SAT 2015 Test.
The table above lists the lengths, to the nearest inch, of a random sample of 21 brown bullhead fish. The outlier measurement of 24 inches is an error. Of the mean, median, and range of the values listed, which will change the most if the 24-inch measurement is removed from the data?
A) Mean
B) Median
C) Range
D) They will all change by the same amount
Answer:A) Mean
B) Median
C) Range
D) They will all change by the same amount
There are a total of 21 values; without the error, 20 values.
Mean with 21 values: $m$
Mean without the error: $(21m-24)/20=m+(m/20-24/20)$.
Since $8<m<24$, then $-0.8<m/20-24/20<0$
Change: from -0.8 to 0
Median with 21 values: the 11th fish is 12.
Median without the error: average of 10h and 11th fish is $(12+12)/2=12$
Change: 0
Range with 21 values: $24-8=16$
Range without the error: $16-8=8$
Change: 8
Answer: C
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SAT 2015 Test.
A group of tenth-grade students responded to a survey that asked which math course they were currently enrolled in.
The survey data were broken down as shown in the table above. Which of the following categories accounts for approximately 19 percent of all the survey respondents?
A) Females taking Geometry
B) Females taking Algebra II
C) Males taking Geometry
D) Males taking Algebra I
There are 310 survey respondents. 19% of 310 is 58.9.
The category with the closest number of students to 58.9 is "males taking Geometry" (59).
Answer: C
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SAT 2015 Test.
Based on the histogram above, of the following, which is closest to the average (arithmetic mean) number of seeds per apple?
A) 4
B) 5
C) 6
D) 7
Answer:A) 4
B) 5
C) 6
D) 7
From the histogram we have that,
2 Apples have 3 seeds each: 6 seeds total;
4 Apples have 5 seeds each: 20 seeds total;
1 Apple have 6 seeds each: 6 seeds total;
2 Apples have 7 seeds each: 14 seeds total;
3 Apples have 9 seeds each: 27 seeds total.
The total number of seeds in 12 apples is $6+20+6+14+27=73$.
Therefore the arithmetic mean is $73/12=6.08$ seeds per apple.
Answer: C
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SAT Practice Test. A researcher wanted to know if there is an association between exercise and sleep for the population of 16 year olds in the United States. She obtained survey responses from a random sample of 2000 United States 16 year olds and found convincing evidence of a positive association between exercise and sleep. Which of the following conclusions is well supported by the data?
A. There is a positive association between exercise and sleep for 16 year olds in the United States.
B. There is a positive association between exercise and sleep for 16 year olds in the world.
C. Using exercise and sleep as defined by the study, an increase in sleep is caused by an increase of exercise for 16 year olds in the United States.
D. Using exercise and sleep as defined by the study, an increase in sleep is caused by an increase of exercise for 16 year olds in the world.
It is given that the survey found convincing evidence of a positive association between exercise and sleep. The population of the study included only 16 year olds in the United States. Therefore, A is correct, and B is wrong.
Alternatives C and D mention cause and effect relationships, which can only be established when participants are assigned to different treatments. Based solely on the results of the survey it is not possible to assert that there is such a cause and effect relationship.
Answer: A
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SAT Practice Test. At a primate reserve, the mean age of all the male primates is 15 years, and the mean age of all female primates is 19 years. Which of the following must be true about the mean age m of the combined group of male and female primates at the primate reserve?
A. $m=17$
B. $m>17$
C. $m<17$
D. $15<m<19$
Answer:
The mean age m of the combined group of male and female primates at the primate reserve will be between 15 and 19 years. If there are a lot more males than females, the mean will be closer to 15; if there are a lot more females than males, the mean will be closer to 19.
Answer: D
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SAT Practice Test. A research assistant randomly selected 75 undergraduate students from the list of all students enrolled in the psychology degree program at a large university. She asked each of the 75 students, “How many minutes per day do you typically spend reading?” The mean reading time in the sample was 89 minutes, and the margin of error for this estimate was 4.28 minutes. Another research assistant intends to replicate the survey and will attempt to get a smaller margin of error. Which of the following samples will most likely result in a smaller margin of error for the estimated mean time students in the psychology degree program read per day?
A. 40 randomly selected undergraduate psychology degree program students
B. 40 randomly selected undergraduate students from all degree programs at the college
C. 300 randomly selected undergraduate psychology degree program students
D. 300 randomly selected undergraduate students from all degree programs at the college
Answer:
The margin of error is related to the inverse of the square root of the sample size:
$Error=\frac{k}{\sqrt{n}}$
Therefore, option A is wrong. Smaller sample sizes provide larger margins of error.
The first sample included only students enrolled in the psychology degree program. If the second sample includes students from all degree programs, it will be a different population than the original survey and therefore the impact to the mean and margin of error cannot be predicted. So options B and D are wrong.
Answer: C
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