1.

Look at the following diagrams. Which diagrams show high linear correlation, moderate or low linear correlation, or no linear correlation?(a) ---Select--- high no moderate or low (b) ---Select--- moderate or low no high (c) ---Select--- no high moderate or low

2.

Look at the following diagrams. Which diagrams show high linear correlation, moderate or low linear correlation, or no linear correlation?(a) ---Select--- high no moderate (b) ---Select--- high moderate no (c) ---Select--- high no moderate

3.

How much should a healthy Shetland pony weigh? Letxbe the age of the pony (in months), and letybe the average weight of the pony (in kilograms).

x	3	6	12	20	23
y	60	95	140	154	185

(a) Make a scatter diagram of the data and visualize the line you think best fits the data.

A scatter diagram has a horizontal axis labeled "x(age (in months))" with values from 3 to 23 and a vertical axis labeled "y(average weight (in kg))" with values from 60 to 185. The scatter diagram has 5 points. A pattern goes up and right from(3, 60)to(23, 185).

A scatter diagram has a horizontal axis labeled "x(age (in months))" with values from 60 to 185 and a vertical axis labeled "y(average weight (in kg))" with values from 3 to 23. The scatter diagram has 5 points. A pattern goes down and right from(60, 23)to(185, 3).

A scatter diagram has a horizontal axis labeled "x(age (in months))" with values from 3 to 23 and a vertical axis labeled "y(average weight (in kg))" with values from 60 to 185. The scatter diagram has 5 points. A pattern goes down and right from(3, 185)to(23, 60).

A scatter diagram has a horizontal axis labeled "x(age (in months))" with values from 60 to 185 and a vertical axis labeled "y(average weight (in kg))" with values from 3 to 23. The scatter diagram has 5 points. A pattern goes up and right from(60, 3)to(185, 23).

(b) Would you say the correlation is low, moderate, or strong? lowmoderate strong

Would you say the correlation is positive or negative? positivenegative

(c) Use a calculator to verify that

x=64,

x²=1118,

y=634,

y²=90,166,

and

xy=9,765.

Computer. (Round your answer to four decimal places.) Asxincreases from 3 to23months, does the value ofrimply thatyshould tend to increase or decrease? Explain your answer. Given our value ofr,yshould tend to decrease asxincreases.Given our value ofr,yshould tend to remain constant asxincreases. Given our value ofr, we can not draw any conclusions for the behavior ofyasxincreases.Given our value ofr,yshould tend to increase asxincreases.

4.

Letxbe the average number of employees in a group health insurance plan, and letybe the average administrative cost as a percentage of claims.

x	3	7	15	40	72
y	40	35	30	28	17

(a)

Make a scatter diagram of the data and visualize the line you think best fits the data.

A scatter diagram has a horizontal axis labeled "x(average number of employees)" with values from 3 to 72 and a vertical axis labeled "y(average cost as percentage)" with values from 17 to 40. The scatter diagram has 5 points. A pattern goes down and right from(13, 40)to(72, 17).

A scatter diagram has a horizontal axis labeled "x(average number of employees)" with values from 3 to 72 and a vertical axis labeled "y(average cost as percentage)" with values from 17 to 40. The scatter diagram has 5 points. A pattern goes up and right from(3, 17)to(72, 40).

A scatter diagram has a horizontal axis labeled "x(average number of employees)" with values from 3 to 72 and a vertical axis labeled "y(average cost as percentage)" with values from 17 to 40. The scatter diagram has 5 points. A pattern goes up and right from(13, 17)to(72, 40).

A scatter diagram has a horizontal axis labeled "x(average number of employees)" with values from 3 to 72 and a vertical axis labeled "y(average cost as percentage)" with values from 17 to 40. The scatter diagram has 5 points. A pattern goes down and right from(3, 40)to(72, 17).

(b)

Would you say the correlation is low, moderate, or strong? positive or negative?

strong and negativestrong and positive moderate and negativelow and negativemoderate and positivelow and positive

(c)

Use a calculator to verify thatx=137,x²=7067,y=150,y²=4798,andxy=3159.Computer. (Round your answer to four decimal places.)

r=

Asxincreases, does the value ofrimply thatyshould tend to increase or decrease? Explain.

Given our value ofr,yshould tend to decrease asxincreases.Given our value ofr, we cannot draw any conclusions for the behavior ofyasxincreases. Given our value ofr,yshould tend to increase asxincreases.Given our value ofr,yshould tend to remain constant asxincreases.

5.

Can a low barometer reading be used to predict maximum wind speed of an approaching tropical cyclone? For a random sample of tropical cyclones, letxbe the lowest pressure (in millibars) as a cyclone approaches, and letybe the maximum wind speed (in miles per hour) of the cyclone.

x	1004	975	992	935	973	920
y	40	100	65	145	77	152

(a) Make a scatter diagram of the data and visualize the line you think best fits the data.

A scatter diagram has a horizontal axis labeled "x(lowest pressure (in millibars))" with values from 920 to 1,004 and a vertical axis labeled "y(maximum wind speed (in mph))" with values from 40 to 152. The scatter diagram has 6 points. A pattern goes down and right from(920, 152)to(1,004, 40).

A scatter diagram has a horizontal axis labeled "x(lowest pressure (in millibars))" with values from 40 to 152 and a vertical axis labeled "y(maximum wind speed (in mph))" with values from 920 to 1,004. The scatter diagram has 6 points. A pattern goes up and right from(40, 920)to(152, 1,004).

A scatter diagram has a horizontal axis labeled "x(lowest pressure (in millibars))" with values from 920 to 1,004 and a vertical axis labeled "y(maximum wind speed (in mph))" with values from 40 to 152. The scatter diagram has 6 points. A pattern goes up and right from(920, 40)to(1,004, 152).

A scatter diagram has a horizontal axis labeled "x(lowest pressure (in millibars))" with values from 40 to 152 and a vertical axis labeled "y(maximum wind speed (in mph))" with values from 920 to 1,004. The scatter diagram has 6 points. A pattern goes down and right from(40, 1,004)to(152, 920).

(b) Would you say the correlation is low, moderate, or strong? lowmoderate strong

Would you say the correlation is positive or negative? positivenegative

(c) Use a calculator to verify that

x=5799,

x²=5,610,059,

y=579,

y²=65,883

and

xy=552,476.

Computer. (Round your answer to four decimal places.) Asxincreases, does the value ofrimply thatyshould tend to increase or decrease? Explain your answer. Given our value ofr, we can not draw any conclusions for the behavior ofyasxincreases.Given our value ofr,yshould tend to increase asxincreases. Given our value ofr,yshould tend to decrease asxincreases.Given our value ofr,yshould tend to remain constant asxincreases.

6.

In baseball, is there a linear correlation between batting average and home run percentage? Letxrepresent the batting average of a professional baseball player, and letyrepresent the player's home run percentage (number of home runs per 100 times at bat). A random sample ofn= 7 professional baseball players gave the following information.

x	0.235	0.249	0.286	0.263	0.268	0.339	0.299
y	1.5	3.1	5.5	3.8	3.5	7.3	5.0

(a)

Make a scatter diagram of the data.

A scatter diagram has a horizontal axis labeled "x(batting average)" with values from 0.235 to 0.34 and a vertical axis labeled "y(home run percentage)" with values from 1.5 to 7.3. The scatter diagram has 7 points. A pattern goes down and right from(0.236, 7.3)to(0.34, 1.5).

A scatter diagram has a horizontal axis labeled "x(batting average)" with values from 1.5 to 7.3 and a vertical axis labeled "y(home run percentage)" with values from 0.235 to 0.34. The scatter diagram has 7 points. A pattern goes down and right from(1.5, 0.34)to(7.3, 0.236).

A scatter diagram has a horizontal axis labeled "x(batting average)" with values from 1.5 to 7.3 and a vertical axis labeled "y(home run percentage)" with values from 0.235 to 0.34. The scatter diagram has 7 points. A pattern goes up and right from(1.5, 0.235)to(7.3, 0.339).

A scatter diagram has a horizontal axis labeled "x(batting average)" with values from 0.235 to 0.34 and a vertical axis labeled "y(home run percentage)" with values from 1.5 to 7.3. The scatter diagram has 7 points. A pattern goes up and right from(0.235, 1.5)to(0.339, 7.3).

(b)

Use a calculator to verify thatx=1.939,x²=0.544,y=29.7,y²=147.09andxy=8.605.

Computer. (Round your answer to four decimal places.)

Asxincreases, does the value ofrimply thatyshould tend to increase or decrease? Explain your answer.

Given our value ofr, we can not draw any conclusions for the behavior ofyasxincreases.Given our value ofr,yshould tend to remain constant asxincreases. Given our value ofr,yshould tend to increase asxincreases.Given our value ofr,yshould tend to decrease asxincreases.

7.

Do larger universities tend to have more property crime? University crime statistics are affected by a variety of factors. The surrounding community, accessibility given to outside visitors, and many other factors influence crime rate. Letxbe a variable that represents student enrollment (in thousands) on a university campus, and letybe a variable that represents the number of burglaries in a year on the university campus. A random sample ofn= 8 universities in California gave the following information about enrollments and annual burglary incidents.

x	11.3	28.0	24.5	14.3	7.5	27.7	16.2	20.1
y	25	78	39	23	15	30	15	25

(a)

Make a scatter diagram of the data. Then visualize the line you think best fits the data.

A scatter diagram has a horizontal axis labeled "x(student enrollment (in thousands))" with values from 7.5 to 28 and a vertical axis labeled "y(annual number of burglaries)" with values from 15 to 78. The scatter diagram has 8 points. A pattern goes down and right becoming less steep from(7.5, 78)to(28, 15).

A scatter diagram has a horizontal axis labeled "x(student enrollment (in thousands))" with values from 15 to 78 and a vertical axis labeled "y(annual number of burglaries)" with values from 7.5 to 28. The scatter diagram has 8 points. A pattern goes up and right from(15, 7.5)to(78, 28).

A scatter diagram has a horizontal axis labeled "x(student enrollment (in thousands))" with values from 7.5 to 28 and a vertical axis labeled "y(annual number of burglaries)" with values from 15 to 78. The scatter diagram has 8 points. A pattern goes up and right from(7.5, 15)to(28, 78).

A scatter diagram has a horizontal axis labeled "x(student enrollment (in thousands))" with values from 15 to 78 and a vertical axis labeled "y(annual number of burglaries)" with values from 7.5 to 28. The scatter diagram has 8 points. A pattern goes down and right becoming less steep from(15, 28)to(78, 7.5).

(b)

Use a calculator to verify thatx=149.6,x²=3206.42,y=250,y²=10734andxy=5439.9.

Computer. (Round your answer to four decimal places.)

Asxincreases, does the value ofrimply thatyshould tend to increase or decrease? Explain your answer.

Given our value ofr,yshould tend to increase asxincreases.Given our value ofr,yshould tend to remain constant asxincreases. Given our value ofr, we can not draw any conclusions for the behavior ofyasxincreases.Given our value ofr,yshould tend to decrease asxincreases.

8.

The correlation coefficientris a sample statistic. What does it tell us about the value of the population correlation coefficient(Greek letter rho)? You do not know how to build the formal structure of hypothesis tests ofyet. However, there is a quick way to determine if the sample evidence based onis strong enough to conclude that there is some population correlation between the variables. In other words, we can use the value ofrto determine if0. We do this by comparing the value |r| to an entry in the correlation table. The value ofin the table gives us the probability of concluding that0 when, in fact,= 0 and there is no population correlation. We have two choices for:= 0.05 or= 0.01.(a) Look at the data below regarding the variablesx= age of a Shetland pony andy= weight of that pony. Is the value of |r| large enough to conclude that weight and age of Shetland ponies are correlated? Use= 0.05. (Round your answer forrto four decimal places.)

x	3	6	12	26	20
y	60	95	140	182	184

r
criticalr

ConclusionReject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated.Reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated. Fail to reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated.Fail to reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated.

(b) Look at the data below regarding the variablesx= lowest barometric pressure as a cyclone approaches andy= maximum wind speed of the cyclone. Is the value of |r| large enough to conclude that lowest barometric pressure and wind speed of a cyclone are correlated? Use= 0.01. (Round your answer forrto four decimal places.)

x	1004	975	992	935	978	930
y	40	100	65	145	67	147

r
criticalr

Conclusion Reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.Reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. Fail to reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.Fail to reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.

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