MATH 140 - 2A - Statistics
This chapter is from Introduction to Statistics for Community College Students,
1st Edition, by Matt Teachout, College of the Canyons, Santa Clarita, CA, USA, and is licensed
under a “CC-By” Creative Commons Attribution 4.0 International license – 10/1/18
Problem Set Section 2A
1. Describe each of the following symbols. What does the symbol represent? Is the symbol describing a sample statistic or a population parameter?
N , n , π , p̂ , μ , x̅ , σ , s , ????????2, ????????2, ρ , r , ????????1 , ????????1
(#2-25) Directions: Determine if the numbers in the following clips from magazines and newspapers are describing a population parameter or a sample statistic. In each case, give the symbol we would use for the parameter or statistic. (N , n , π , p̂ , μ , x̅ , σ , s , ????????2, ????????2, ρ , r , ????????1 , ????????1)
2. “Our study found that of the 200 people tested in the sample, only 3\% showed side effects to the medication.”
3. “It has been speculated for years that the mean average height of all men is 69.2 inches, but our sample data disagrees with this. Our sample mean average was 69.5 inches.”
4. “The standard deviation for all humans is about 1.8 degrees Fahrenheit. A random sample of 52 people found a standard deviation of 1.739 degrees Fahrenheit”.
5. “We tested a sample of 300 incoming college freshman and found that their mean average IQ was 101.9 with a standard deviation of 14.8”.
6. “The mean average human body temperature has long been thought to be 98.6 degrees Fahrenheit, but our sample of 63 randomly selected adults had a mean average was 98.08”.
7. “The mean average number of units that students take per semester is about 12, but when we took a random sample of 160 college students found that the mean average was 12.37 units.”
8. “A public opinion poll showed that 47.2\% of voters would vote for the candidate, but when the votes or entire population were counted we found that only 41.3\% voted for the candidate.”
9. “According to the California Department of Finance, the Los Angeles county population as of January 2015 was approximately 10,136,559 people.”
10. “We want to check and see if the population correlation coefficient could be zero. The sample correlation coefficient was 0.338.”
11. “Many experts think that the population slope for weight gain in these type of bears is about 3 pounds per month, but the sample slope from 54 bears was 2.7055 pounds per month.”
12. “A random sample of 40 men found that the sample variance for systolic blood pressure was 109.474, but this indicates that the population variance could be as high as 173.”
13. “According to the 2015 U.S. census, approximately 78\% of U.S. households own a computer. A random sample of 165 households found that 81.2\% of them owned a computer.”
14. “We think that the population correlation coefficient is zero. The sample correlation coefficient was 0.0371.”
15. “IQ tests are supposed to have a population mean of 100 and a population standard deviation of 15 IQ points. This could be correct since our random sample data had a mean of 97.7 and the standard deviation of 15.3 IQ points.”
16. “When analyzing the relationship between the amount of mercury and the pH of Florida lakes, we found a sample slope of −0.152. We are wondering if the population slope could be zero.”
17. “We believe that the population mean average pH of Florida lakes is approximately 6.7, yet our sample data from 53 randomly selected lakes had a mean of 6.591.”
18. “While the sample variance is 37.882, we think the population variance could be as high as 50.”
This chapter is from Introduction to Statistics for Community College Students,
1st Edition, by Matt Teachout, College of the Canyons, Santa Clarita, CA, USA, and is licensed
under a “CC-By” Creative Commons Attribution 4.0 International license – 10/1/18
19. “We believe there are approximately 59,530 people currently living in Canyon Country, CA.”
20. “A random sample of 60 adults found that 21.7\% of them had this characteristic. However, we think the population percentage is probably closer to 15\%.”
21. “The mean average weight of the 10 male lions was 437.2 pounds. Most people believe that the mean average weight of all male lions is closer to 420 pounds.”
22. “The correlation coefficient for the ordered pair sample data was 0.922. This seems very significant, but does this indicate that the population correlation coefficient is 1?”
23. “We analyzed the gas usage and distance for large 18-wheeler trucks and found the sample slope to be 6.23 miles per gallon. Articles online indicate that the population slope for all 18-wheeler trucks is closer to 5.9 miles per gallon.”
24. “The sample standard deviation was approximately $3.78. We want to see if the population standard deviation could be $3.50.”
25. “A random sample of 38 cars, found that the mean average displacement was 177.289 and the standard deviation was 88.877.”
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Problem Set 2A
1. Describe each of the following symbols. What does the symbol represent? Is the
symbol describing a sample statstc or a populaton parameter? N , n , π , , μ , x̅ , σ , p̂
s , 𝜎𝜎2, 𝑠𝑠2, ρ , r , 𝛽𝛽1 , 𝑏𝑏1
𝜎𝜎2: Parameter describing a populaton variance.
𝑠𝑠2: Statstc describing a sample variance.
N: Parameter describing the size of a populaton.
n: Statstc describing the size of a sample.
π or p: Parameter describing a populaton proporton.
: Statstc describing a sample proporton. p̂
μ: Parameter describing a populaton mean average.
x̅ : Statstc describing a sample mean average.
σ: Parameter describing a populaton standard deviaton.
ρ: Parameter describing a populaton correlaton coefficient.
r: Statstc describing the correlaton coefficient from sample data.
𝛽𝛽1: Parameter describing a populaton slope.
𝑏𝑏1: Statstc describing a slope from sample data.
2. “Our study found that of the 200 people tested in the sample, only 3\% showed side
effects to the medicaton.” N=200 p=0.03
3. “It has been speculated for years that the mean average height of all men is 69.2 inches,
but our sample data disagrees with this. Our sample mean average was 69.5 inches.” μ
= 69.2 inches (parameter) x̅ = 69.5 inches (statstc)
4. The standard deviaton for all humans is about 1.8 degrees Fahrenheit. A random
sample of 52 people found a standard deviaton of 1.739 degrees Fahrenheit”.
This study source was downloaded by 100000821021791 from CourseHero.com on 08-04-2021 19:13:03 GMT -05:00
https://www.coursehero.com/file/90271572/Problem-Set-2Adocx/
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https://www.coursehero.com/file/90271572/Problem-Set-2Adocx/
5. We tested a sample of 300 incoming college freshman and found that their mean
average IQ was 101.9 with a standard deviaton of 14.8”. n = 300 students (statstc). x̅
= 101.9 IQ (statstc). s = 14.8 IQ (statstc)
6. The mean average human body temperature has long been thought to be 98.6 degrees
Fahrenheit, but our sample of 63 randomly selected adults had a mean average was
98.08”.
7. “The mean average number of units that students take per semester is about 12, but
when we took a random sample of 160 college students found that the mean average
was 12.37 units.” μ = 12 units (parameter)
n = 160 students (statstc) x̅ = 12.37 units (statstc)
8. A public opinion poll showed that 47.2\% of voters would vote for the candidate, but
when the votes or entre populaton were counted we found that only 41.3\% voted for
the candidate.” N = 10,136,559 people (parameter)
9. According to the California Department of Finance, the Los Angeles county populaton
as of January 2015 was approximately 10,136,559 people.”
10. “We want to check and see if the populaton correlaton coefficient could be zero. The
sample correlaton coefficient was 0.338.”
11. n= 54 bears (statstc) 𝑏𝑏 = 2.7055 pounds per month (Statstc) 𝛽 𝛽=3 pounds per month
(Parameter)
12. “Many experts think that the populaton slope for weight gain in these type of bears is
about 3 pounds per month, but the sample slope from 54 bears was 2.7055 pounds per
month. n=54
13. “A random sample of 40 men found that the sample variance for systolic blood pressure
was 109.474, but this indicates that the populaton variance could be as high as 173.” π
= 0.78 (parameter) n = 165 households (statstc) =0.812(statstc) p̂
14. “According to the 2015 U.S. census, approximately 78\% of U.S. households own a
computer. A random sample of 165 households found that 81.2\% of them owned a
computer.” N=165
15. “We think that the populaton correlaton coefficient is zero. The sample correlaton
coefficient was 0.0371.” 100 IQ (parameter) 15 IQ (parameter) 97.7 IQ (statstc) 15.3 IQ
(statstc)
16. “IQ tests are supposed to have a populaton mean of 100 and a populaton standard
deviaton of 15 IQ points. This could be correct since our random sample data had a
mean of 97.7 and the standard deviaton of 15.3 IQ points.”
17. “When analyzing the relatonship between the amount of mercury and the pH of
Florida lakes, we found a sample slope of −0.152. We are wondering if the populaton
slope could be zero.” x̅ =6.7 pH (parameter) 53 lakes (statstc) 6.591 pH (statstc) n= 53
lakes(Statcsts). μ= 6.7ph(Parameter)
This study source was downloaded by 100000821021791 from CourseHero.com on 08-04-2021 19:13:04 GMT -05:00
https://www.coursehero.com/file/90271572/Problem-Set-2Adocx/
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https://www.coursehero.com/file/90271572/Problem-Set-2Adocx/
18. We believe that the populaton mean average pH of Florida lakes is approximately 6.7,
yet our sample data from 53 randomly selected lakes had a mean of 6.591.”
19. While the sample variance is 37.882, we think the populaton variance could be as high
as 50.” N = 59,530 people (parameter)
20. “We believe there are approximately 59,530 people currently living in Canyon Country,
CA.” n=59,530
21. A random sample of 60 adults found that 21.7\% of them had this characteristc.
However, we think the populaton percentage is probably closer to 15\%.” n = 10 lions
(statstc) x̅ = 437.2 pounds (statstc) μ = 420 pounds (parameter)
22. The mean average weight of the 10 male lions was 437.2 pounds. Most people believe
that the mean average weight of all male lions is closer to 420 pounds.”
23. “The correlaton coefficient for the ordered pair sample data was 0.922. This seems
very significant, but does this indicate that the populaton correlaton coefficient is 1?”
𝑏𝑏= 6.23 mpg (Statstc) 𝛽𝛽 = 5.9 mpg (Parameter)
24. We analyzed the gas usage and distance for large 18-wheeler trucks and found the
sample slope to be 6.23 miles per gallon. Artcles online indicate that the populaton
slope for all 18-wheeler trucks is closer to 5.9 miles per gallon.”
25. the sample standard deviaton was approximately $3.78. We want to see if the
populaton standard deviaton could be $3.50.” n = 38 cars (statstc)
x̅ = 177.289 displacement (statstc) s = 88.877 displacement (statstc)
26. A random sample of 38 cars, found that the mean average displacement was 177.289
and the standard deviaton was 88.877.” n = 38 cars (statstc)
x̅ = 177.289 displacement (statstc) s = 88.877 displacement (statstc
This study source was downloaded by 100000821021791 from CourseHero.com on 08-04-2021 19:13:04 GMT -05:00
https://www.coursehero.com/file/90271572/Problem-Set-2Adocx/
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