MATH 140 - 2A

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/

Th is

stu dy

re so

ur ce

w as

sh ar

ed v

ia C

ou rs

eH er

o. co

m

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/

Th is

stu dy

re so

ur ce

w as

sh ar

ed v

ia C

ou rs

eH er

o. co

m

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/

Th is

stu dy

re so

ur ce

w as

sh ar

ed v

ia C

ou rs

eH er

o. co

m

Powered by TCPDF (www.tcpdf.org)