Unit 5

Which two events are independent?

A and X

Vehicles passing over a bridge have two options for paying their bridge toll: paying with a live cashier or using a Speed Pass device affixed to the dashboard. Data on a busy day for cars and trucks passing over the bridge are shown here. Payment Method Live CashierSpeed PassTotalVehicle TypeCar3567102Truck184765 Total53114167 What proportion of vehicles crossing the bridge are trucks and use Speed Pass?

0.2814

The two-way table shows the number of books of each type in Eliza's home. What is the probability that a randomly selected reference book is hardcover?

0.4

A movie theater offers three types of tickets: child, student, and adult. Ticket sales for two movies are shown in the table. Ticket Type ChildStudentAdultTotalMovie TitleThe Ransom123870100Space Force344256132 Total4680126232 What proportion of tickets sold were adult tickets?

0.5431

An official for a regional baseball league examines attendance data for teams in the league. For each team in the league, the number of losses and the average game attendance is shown in the scatterplot. The value of r for the scatterplot is -0.847. Which of these data combinations weakens the correlation?

2 losses, 15.2 thousand fans

A statistics student wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. The given data lists the number of absences and GPAs for 15 randomly selected students. Using technology, what is the correlation?

-0.56

The two-way table shows the number of houses on the market in the Castillos' price range. What is the probability that a randomly selected house with 2 bathrooms has 3 bedrooms?

0.8

A certain standardized test measures students' knowledge in English and math. The English and math scores for 10 randomly selected students are given in the table. Using technology, what is the correlation coefficient?

0.91

The table shows the results of a survey of 400 random people on whether they like liquid soap, bar soap, or both. Which is the marginal relative frequency for the people who do not like bar soap?

100/400

The two-way frequency table represents data from a survey asking a random sampling of people whether they can see the sunrise or sunset from the front of their home. Which is the joint relative frequency for the people who can only see the sunset?

12/38

The average daily print circulation for the Philadelphia Inquirer, a local newspaper, has declined each year since the year 2000. To develop a model for estimating circulation each year, the log of circulation (in thousands) was computed and plotted for a number of years since 2000. Using the scatterplot and computer output, a reasonable estimate of the average daily print circulation in the year 2013 is:

121.6 thousand because and 102.085 = 121.6

A sports-equipment researcher was interested in the relationship between the speed of a golf club (in feet per second) and the distance a golf ball travels (in yards). Information was collected on several golfers and was used to obtain the regression equation ŷ = 2x - 106, where x represents the club speed and ŷ is the predicted distance. What is the predicted distance of a ball that is hit with a club speed of 168 ft/sec?

230 yards

A biologist is studying the relationship between the mass of brains found in mammals taken from a forest and the body mass of the mammals. A sample of 14 such mammals was taken. The equation of the least-squares line for the relationship between brain mass and body mass is computed as . Based on the residual plot, is a linear model appropriate for describing the relationship between brain mass and body mass?

A linear model is not appropriate, because there is a clear pattern shown in the residual plot.

A punter for a football team is trying to determine the optimal angle for striking the football off his foot—this is called the launch angle. Using video, his coach records a number of punts kicked using different launch angles and the height in feet for each punt. Using computer software, the coach achieves a linear model by taking the log of each launch angle and plotting against the log of each height. Based on the scatterplot and residual plot, which type of model would best summarize the relationship between launch angle and punt height?

A power model is appropriate because the scatterplot of log angle and log height is roughly linear.

A group of students and workers entering a metro station were asked whether they were riding the bus or the subway. The two-way table shows their answers. How many people were polled?

166

A statistics student wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. The given data lists the number of absences and GPAs for 15 randomly selected students. Using technology, what is the equation for the least-squares regression line?

ŷ = 3.79 - 0.10x

The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The results are given in the table. Using technology, what is the y-intercept and what is its interpretation?

The y-intercept is 17.37. When the weight is 0 pounds, it does not make sense to interpret the height.

To investigate the influence of distracted driving, 13 volunteers were asked to participate in a study involving a driving simulator. The participants drove at a safe speed but were told to stop the car at a random moment during the simulation. The scatterplot shows the reaction time and the simulated car's stopping distance, in feet, for each volunteer. Which point most likely decreases the correlation shown in the scatterplot?

reaction time 2 seconds, stopping distance 67 feet

Find P(Y|B) from the information in the table. To the nearest tenth, what is the value of P(Y|B)?

0.4

At the Kansas City Airport, a group of pilots for Skyways and Yellow Jet airlines were asked whether their flights were flying east or west. The two-way table shows their answers. Flight Directions Which joint frequency has the most flights?

Yellow Jet, going east

A relative frequency table is made from data in a frequency table. What is the value of k in the relative frequency table? Round the answer to the nearest percent.

11%

Based on the scatterplot below, what is the most likely value for "Pounds of Apples" when "Number of Apples" is 80?

42

A statistics teacher was interested in the relationship between the number of days students waited to start a project and the score that project received (out of 100 points). Information was collected on several students and was used to obtain the regression equation ŷ = -3.64x + 96.5, where x represents the number of procrastination days and ŷ is the predicted grade. What is the predicted grade of a student who procrastinated for 2 days?

89.22

A certain standardized test measures students' knowledge in English and math. The English and math scores for 10 randomly selected students are given in the table. Using technology, the slope of the least-squares regression line is

0.68, which means for each additional point in the English score, the math score is predicted to increase by 0.68 points.

A soccer coach surveyed the players to determine the number of players who preferred selling coupon books, magazine subscriptions, or both for their fundraiser. The results are given in the Venn diagram. To the nearest whole percent, what is the value of a in the relative frequency table for the survey results?

a = 27%

A student collected data on the size of coffee chosen by customers at a convenience store, and whether the customers took their coffee with cream, sugar, or both. Size of Coffee SmallMediumLargeTotalCoffee AdditiveCream8152144Sugar481123Both15234280 Total274674147 Given that a customer likes both cream and sugar, what is the probability that the customer chose a large coffee?

52.5%

A real estate agent would like to develop a model for predicting sale price of homes in a suburban area. One variable that can be useful for predicting home value is home interior size, which is measured in square feet. Using 13 homes sold recently in the area, the real estate agent uses software to find a least-square line to summarize the relationship. The resulting equation is . Based on the scatterplot and residual plot shown, is a linear model appropriate for summarizing the relationship?

A linear model is appropriate because the residual plot shows no pattern

Graduation rate is one measure used to compare colleges in national publications. One such publication compared semester tuition against graduation rate, defined as the percentage of students who graduate within four years. The value of r for the scatterplot is 0.856. Which of the following is an appropriate summary of the scatterplot?

Colleges with higher tuition tend to have higher graduation rates.

According to the scatterplot below, which statement is correct?

The input, or independent variable, is years in operation.

Tyrese graphed the scatterplot below to show the weight and the number of apples he picked.There is a relationship between the variables, because as the number of apples increases, the weight of the apples

increases

Which statement is true about whether C and Y are independent events?

C and Y are not independent events because P(C∣Y) ≠ P(C).

Which describes a correct way to construct a scatterplot?

When analyzing the number of home runs that a baseball player hit over several seasons, the season is the independent variable.

Market researchers were interested in the relationship between the number of pieces in a brick-building set and the cost of the set. Information was collected from a survey and was used to obtain the regression equation ŷ = 0.08x + 1.20, where x represents the number of pieces in a set and ŷ is the predicted price (in dollars) of a set. What is the predicted price of a set that has 500 pieces?

$41.20

One statistic used to measure a country's wealth is its gross domestic product (GDP). A higher GDP indicates greater wealth in the country. A researcher compared the GDP per person for 12 countries with the life expectancy of that country. The data for the 12 countries are shown in the scatterplot. The value of r for the scatterplot is 0.608. Which of the following statements accurately describes the relationship shown in the scatterplot?

Countries with higher GDPs tend to have higher life expectancies.

A group of 120 people were asked whether their income level is above or below $25,000 and whether they subscribe to a movie channel. The data from the survey is shown in the Venn diagram. Use the Venn diagram to find the missing values in the frequency table. Which shows the correct values for the variables in the table?

a = 34, b = 18, c = 68

A student collected data on the size of coffee chosen by customers at a convenience store, and whether the customers took their coffee with sugar, cream, or both. Size of Coffee SmallMediumLargeTotalCoffee AdditiveCream8152144Sugar481123Both15234280 Total274674147 What percentage of customers chose a medium-sized coffee?

31.3%

The scatterplot below was created from a table of values and represents the relationship between the number of seconds spent doing sit-ups and the number of sit-ups completed for some of the members of a physical education class. Assuming that none of the data points overlap and that all the data points were plotted, how many data points were in the table?

8

A residential community was polling households to find out whether they wanted to get their TV signal from a satellite or cable. The results are shown in the Venn diagram. What are the values of a and b in the relative frequency table for the survey results? Round answers to the nearest percent.

a = 38%, b = 3%

Market researchers were interested in the relationship between the price of bobbleheads and the demand of bobbleheads. Information was collected from a survey and used to obtain the regression equation ŷ = -0.227x + 50.455, where x represents the price of bobbleheads (measured in dollars) and ŷ is the predicted demand of bobbleheads (in units). What is the predicted demand of a bobblehead that has price of $6.00?

49.093 units

A sports-equipment researcher was interested in the relationship between the speed of a golf club (in feet per second) and the distance a golf ball travels (in yards). Information was collected on several golfers and was used to obtain the regression equation ŷ = 2x - 106, where x represents the club speed and ŷ is the predicted distance. Which statement best describes the meaning of the slope of the regression line?

For each increase in club speed by 1 ft/sec, the predicted distance increases by 2 yards.

Market researchers were interested in the relationship between the price of bobbleheads and the demand of bobbleheads. Information was collected from a survey and was used to obtain the regression equation ŷ = -0.277x + 50.455, where x represents the price of a bobblehead (measured in dollars) and ŷ is the predicted demand of bobbleheads (in units). Which statement best describes the meaning of the slope of the regression line?

For each increase in price by $1, the predicted demand decreases by 0.227 units.

Which is the last step when creating and analyzing a scatterplot from a table of values?

Identify if there is a relationship between the independent and dependent variables.

A fast-food restaurant kept information about the drinks that were ordered along with the different-sized kids' meals, as shown in the table. Which statements are true? Select three options.

Sixty-three of the orders of soda came with a regular-sized meal. A total of 124 large-sized meals were ordered. Milk was requested for 16 of the large-sized meal orders

Graduation rate is one measure used to compare colleges in national publications. One such publication compared semester tuition against graduation rate, defined as the percentage of students who graduate within four years. The value of r for the scatterplot is 0.856. How would the correlation change if the graduation rate was plotted on the x-axis and tuition plotted on the y-axis?

The correlation would stay the same.

A nutritionist collects data from 25 popular breakfast cereals. For each cereal, the number of calories per serving is plotted on the x-axis against the number of milligrams of sodium on the y-axis. The value of r for the resulting scatterplot is 0.83. Which of the following is a correct interpretation of this value?

There is a positive relationship between calories and sodium. The relationship is strong.

A statistics teacher was interested in the relationship between the number of days students waited to start a project and the score that project received (out of 100 points). Information was collected on several students and was used to obtain the regression equation ŷ = -3.64x + 96.5, where x represents the number of procrastination days and ŷ is the predicted grade. Which statement best describes the meaning of the y-intercept of the regression line?

When the number of procrastination days is 0, the predicted grade is 96.5 points.

As people exited a movie theater, they were informally surveyed about whether they enjoyed the movie or not. Males Enjoyed: 47Did not enjoy: 13 Females Enjoyed: 53Did not enjoy: 3 What are the values of a and b in the relative frequency table for the survey results? Round answers to the nearest percent.

a = 41%, b = 3%

Food services for a school district examined the choices of side dish for students at three types of schools in the district: elementary school, middle school, and high school. Side Dish Chosen French FriesCarrot SticksApple WedgesTotalType of SchoolElementary853523143Middle564231129High474536128 Total18812290400 Given that a student chose apple wedges, what is the probability that the student is in high school?

40.0%

Fuel efficiency, measured in miles per gallon, is a feature often considered by shoppers looking for a new car. The scatterplot shows the vehicle weight of 15 car models in pounds, plotted against their highway fuel efficiency. Which of the following is a reasonable value for r, given the relationship shown in the scatterplot?

-0.898

Passengers traveling by airplane have two options for their bags: carry-on (for smaller bags) or check (for large bags). An airline examines the baggage choices of its customers on a selection of short flights (less than 500 miles) and long flights (more than 500 miles). Length of Flight ShortLongTotalBaggageOptionsCarry-on342259601Check178311489Neither533285 Total5736021175 What is the probability that a customer is on a short flight, given that the customer has a carry-on bag?

342/602

Willis has noticed that when time has been one of the variables analyzed by a scatterplot he has looked at, it has always been the independent variable. He has hypothesized that time can never be a dependent variable. Does the scatterplot below confirm or invalidate Willis's hypothesis?

It invalidates his hypothesis because it is possible for the time a trip takes to depend on the distance that is traveled during the trip.

An official for a regional baseball league examines attendance data for teams in the league. For each team in the league, the number of losses and the average game attendance are shown in the scatterplot. The value of r for the scatterplot is -0.847. Which statement best describes the association shown in the scatterplot?

Losses and attendance have a strong, negative association.

Graduation rate is one measure used to compare colleges in national publications. One such publication compared semester tuition against graduation rate, defined as the percentage of students who graduate within four years. Which statement best explains the relationship between the variables?

More selective colleges tend to have higher tuition and higher graduation rates.

A statistics teacher was interested in the relationship between the number of days students waited to start a project and the score that project received (out of 100 points). Information was collected on several students and was used to obtain the regression equation ŷ = -3.64x + 96.5, where x represents the number of procrastination days and ŷ is the predicted grade. What is the predicted grade of a student who procrastinated for 1 week?

71.02

When a scatterplot is created from a table of values, which statement is correct?

It is possible for two points to have the same x-coordinate and the same y-coordinate.

Kevin went fishing and is using a scatterplot to analyze the relationship between the weight of each of the fish he caught in pounds and in kilograms. He uses the weight in pounds as the independent variable and the weight in kilograms as the dependent variable. Which statement is correct?

The points on the scatterplot will go up from left to right because as the weight in pounds increases, the weight in kilograms increases.

A forest management agency collects measurements from beech trees in a public park. The age of many of the trees is known, and the basal area—the area of land occupied by the trunks of the trees—is also measured. A least-squares equation that compares the basal area to the age of each tree is given by . Based on the residual plot shown, is a linear model appropriate for comparing tree age to basal area?

Because the residual plot does not show a clear pattern, a linear model is appropriate.

How many variables are displayed in a scatterplot?

one along the x-axis, and one along the y-axis

A certain standardized test measures students' knowledge in math and English. The scatterplot displays the scores for 10 randomly selected students. The equation ŷ = 54.16 + 0.87x is called the least-squares regression line because it

makes the sum of the squared residuals as small as possible.

Passengers traveling by airplane have two options for their bags: carry-on (for smaller bags) or check (for large bags). An airline examines the baggage choices of its customers on a selection of short flights (less than 500 miles) and long flights (more than 500 miles). Length of Flight ShortLongTotalBaggageOptionsCarry-on342259601Check178311489Neither533285 Total5736021175 What is the probability that a customer is on a short flight and checked their bag?

15.1%

Car rideshare services are a popular option for people needing to move about in large cities. The scatterplot shows the distances of trips and fares, in dollars, for an adult living in a city over a period of a month. The value of r for the scatterplot is 0.950. How would the value of the correlation coefficient change if the fares were plotted on the x-axis and distances on the y-axis?

The value of the correlation coefficient would not change.

An online store sold a gift basket at five different prices and recorded the number of gift baskets that were sold at each price. The results are shown in the scatterplot. Which statement is correct based on the scatterplot?

There is a relationship between price and gift baskets sold, and the relationship is that as the price increases, the gift baskets sold decreases.

Car rideshare services are a popular option for people needing to move about in large cities. The scatterplot shows the distances and fares, in dollars, for an adult living in a city over a month period. The value of r for the scatterplot is 0.950. Which of the labeled points weakens the overall association between distance and fare?

point A

The scatterplot displays the number of pretzels students could grab with their dominant hand and their handspan, measured in centimeters. An analysis was completed and the computer output is shown. PredictorCoefSE Coeft-ratiopConstant-14.714.3171.6890.046Handspan1.5850.3105.1140.000 S = 3.05R-Sq = 52.1%R-Sq(Adj) = 51.7% Using the computer output, what is the equation of the least-squares regression line? PredictorCoefSE Coeft-ratiopConstant-14.714.3171.6890.046Handspan1.5850.3105.1140.000 S = 3.05R-Sq = 52.1%R-Sq(Adj) = 51.7%

ŷ = -14.71 + 1.585x

Information about the recycling drive at school is shown in the table. Let A be the event that the item pulled out of the recycling bin is a plastic bottle, and let B be the event that a tenth grader recycled that item. Which statement is true about whether A and B are independent events?

A and B are not independent events because P(A∣B) ≠ P(A).

A popular board game manufacturer was interested in the relationship between the amount of time it takes to play a game and how well that game is rated among board game players. Information was collected on several board games, and was used to obtain the regression equation ŷ = 27.273x + 18.182, where x represents time it takes to play (in hours) and ŷ is the predicted rating of that game (in points). What is the predicted rating of a game that takes 90 minutes to play?

59.0915 points

One statistic used to measure a country's wealth is the gross domestic product (GDP). A higher GDP indicates higher wealth. A researcher compared the GDP per person for 12 countries with the life expectancy of that country. The data for the 12 countries are shown in the scatterplot. The value of r for the scatterplot is 0.608. How does the country of Jordan, labeled in the graph, influence the correlation?

This data point weakens the correlation.

Belleville High School offers classes on three different foreign languages. Let A be the event that a student is in eleventh grade, and let B be the event that a student is enrolled in French class. Which statement is true about whether A and B are independent events?

A and B are independent events because P(A∣B) = P(A).

A survey was taken of children between the ages of 7 and 12. Let A be the event that the person rides the bus to school, and let B be the event that the person has 3 or more siblings. Which statement is true about whether A and B are independent events?

A and B are not independent events because P(A∣B) = 0.375 and P(A) = 0.25.

Many new cars provide detailed information about engine performance on the dashboard. One such feature allows drivers to observe current fuel efficiency, recorded in miles per gallon, as they drive. A consumer takes a long trip driving at different speeds, while a passenger records both driving speed in miles per hour and fuel efficiency for a number of selected points along the trip. A least-squares equation that relates speed to fuel efficiency is given by . Based on the residual plot shown, is a linear model appropriate for comparing driving speed and fuel efficiency?

A linear model is not appropriate because the residual plot shows a clear pattern.

Many Texas cities have experienced substantial growth in population over the last 20 years. The growth of Houston, Texas, since 2015 is shown in the scatterplot. A least-squares equation that relates the number of years since 2015 to the population of that year (in millions) is given by . Based on the residual plot, is a linear model suitable for modeling the population growth of Houston?

A linear model is not suitable because the residual plot shows a curved pattern.

In the decathlon event at large track meets, male athletes compete in a total of 10 events. Their combined performance in each of the events is used to determine the winner. Two of the events are the 200-meter dash and the javelin throw. For 12 athletes at a large international competition, performances in these events are recorded and placed in a scatterplot. The performance for one athlete from Latvia is labeled in the graph. How does this point influence the correlation of the scatterplot?

This data point weakens the correlation.

A health organization collects data on hospitals in a large metropolitan area. The scatterplot shows the relationship between two variables the organization collected: the number of beds each hospital has available and the average number of days a patient stays in the hospital (mean length of stay). Which hospital represented in the scatterplot would be considered a high leverage point?

the hospital with 310 beds

A group of 55 football players was polled about which synthetic grass they like to play on, Chemgrass or Chemstrand. The data from the survey is shown in the Venn diagram. Use the Venn diagram to find the missing values in the frequency table. What are the values of x, y, and z?

x = 13, y = 17, and z = 15

Yolanda wanted to see if there was a connection between red hair and green eyes. She observed people walking past her on the street and noted their hair and eye color. Red HairGreen eyes: 18Eye color other than green: 29 Hair Color Other Than RedGreen eyes: 114Eye color other than green: 650 Consider the relative frequency table. To the nearest whole percent, what is the value of x in the table?

x = 14%

One drive-through car wash facility offers three different types of washes: basic, deluxe, and supreme. The manager of the car wash facility tallies customer selections over three days: Type of Car Wash BasicDeluxeSupremeTotalDayFriday15431977Saturday275222101Sunday23451987 Total6514060265 What proportion of customers selected the deluxe car wash? 0.1698 0.2264 0.5283 0.5584

0.5283

The members of a high school band asked a number of students whether they would like blue, gold, or both for the uniforms for the band. The results are given in the Venn diagram. What are the values of a and b in the relative frequency table for the survey results? Round answers to the nearest percent.

a = 33%, b = 43%

The arm span and foot length were measured (in centimeters) for each of the 19 students in a statistics class and displayed in the scatterplot. An analysis was completed and the computer output is shown. PredictorCoefSE Coeft-ratiopConstant-7.6112.5672.9650.046Arm span0.1860.0355.3770.000 S = 1.61R-Sq = 63.0%R-Sq(Adj) = 62.7% Using the computer output, the slope of the least-squares regression line means for each additional centimeter in

arm span, foot length is predicted to increase by about 0.186 cm.

The scatterplot displays the number of pretzels students could grab with their dominant hand and their handspan, measured in centimeters. An analysis was completed and the computer output is shown. PredictorCoefSE Coeft-ratiopConstant-14.714.3171.6890.046Handspan1.5850.3105.1140.000 S = 3.05R-Sq = 52.1%R-Sq(Adj) = 51.7% Using the computer output, the slope of the least-squares regression line means for each additional

centimeter in handspan, the number of pretzels is predicted to increase by about 1.585.

As an object travels away from a light source, the intensity of the light on the object diminishes. To measure the influence of distance on light intensity, a student uses a light meter to record intensity, in lumens, from a source at various distances. The results, which compare distance in centimeters to the recorded light intensity, are shown in the scatterplot. To develop a linear model, the student next took the log of each distance and the log of each intensity and used computer software to find a least-square equation, shown in the computer output. Using the computer output, the best estimate of the light intensity at 19 centimeters is:

0.0876, because 0.8561 − 1.4966(log 19) = −1.058, and 10−1.058=0.0876 lumens.

The scatterplot displays the number of pretzels students could grab with their dominant hand and their handspan, measured in centimeters. An analysis was completed and the computer output is shown. PredictorCoefSE Coeft-ratiopConstant-14.714.3171.6890.046Handspan1.5850.3105.1140.000 S = 3.05R-Sq = 52.1%R-Sq(Adj) = 51.7% Using the computer output, what is the correlation coefficient?

0.722

Vehicles passing over a bridge have two options for paying their bridge toll: paying with a live cashier or using a Speed Pass device affixed to the dashboard. Data on a busy day for cars and trucks passing over the bridge are shown here. Payment Method Live CashierSpeed PassTotalVehicle TypeCar3567102Truck184765 Total53114167 What percentage of vehicles are trucks, given that they use Speed Pass?

41.2%

A sample of adults was asked to choose their favorite sport to watch from a list of four sports. Age Range 18-3031-5051+TotalSportFootball15191751Baseball7121837Basketball1581134Soccer129627 Total494852149 Given that an adult likes soccer, what is the probability the adult is aged 18-30?

44.4%

A school administrator asks each student if they participate in a sport and if they participate in a club. The results are shown below. Participates in a Sport YesNoTotalParticipates in a ClubYes6204501070No325535860 Total9459851930 What percentage of students do not participate in a sport?

51.0%

Mr. Carandang sold a total of 1,790 prints of one of his drawings. Out of all 1,273 unframed prints that he sold, 152 were small and 544 were medium-sized. Out of all of the framed prints that he sold, 23 were small and 42 were extra large. Of the large prints that he sold, 188 were framed and 496 were unframed. SmallMediumLargeExtra LargeTotalFramed 23 264 188 42 ?Unframed 152 544 496 81 1,273Total 175 808 684 123 1,790 Which number is missing from the two-way table?

517

Online entertainment streaming services have gained in popularity in recent years as an alternative to traditional television. One such company has seen steady growth in each period of 3 months, called a quarter, over the past 4 years. The scatterplot shows the relationship between the number of quarters since January 2014 and the log of the number of members to the streaming service. A least-squares equation that summarizes this relationship is . Based on the scatterplot and residual plot, what type of model is appropriate for comparing time and subscribers?

An exponential model is appropriate because the relationship between period and the log of subscribers is roughly linear and the residual plot shows no distinct pattern.

The arm span and foot length were measured (in centimeters) for each of the 19 students in a statistics class and displayed in the scatterplot. An analysis was completed, and the computer output is shown. PredictorCoefSE Coeft-ratiopConstant-7.6112.5672.9650.046Arm span0.1860.0355.3770.000 S = 1.61R-Sq = 63.0%R-Sq(Adj) = 62.7% Using the computer output, what is the equation of the least-squares regression line?

ŷ = -7.611 + 0.186x

Wyatt wants to study the relationship between the number of siblings that a student has and the student's grade-point average using a scatterplot. He believes that if the points form a straight line, then there is a relationship between the two variables. Which scatterplot proves that Wyatt's statement is not always true?

B. Constant

Suppose there is a relationship between independent and dependent variables represented by a scatterplot. Which statement is correct?

The independent variable influences change in the dependent variable whether the points on the scatterplot go up or down from left to right.

The daily print publication of newspapers has declined in many large cities over the past 25 years. The Philadelphia Inquirer weekday print circulation was at its highest in 2001, with an average daily circulation of 226,000 copies, and has decreased every year since then. To develop a linear model for estimating yearly circulation, the log of the daily circulation in thousands was taken. Based on the scatterplot of the transformed data and the residual plot, which type of model is appropriate for estimating print publication each year?

An exponential model is appropriate because the scatterplot of years and the log of circulation is roughly linear and the residual plot shows no distinct pattern.

A school administrator asks each student if they participate in a sport and if they participate in a club. The results are shown below. Participates in a Sport YesNoTotalParticipates in a ClubYes6204501070No325535860 Total9459851930 Given that a student participates in a sport, what is the probability that the student also participates in a club?

0.6561

The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The measurements are given in the table. Using technology, what is the equation for the least-squares regression line?

ŷ = 17.37 + 0.50x

A movie production company was interested in the relationship between the budget to make a movie and how well that movie was received by the public. Information was collected on several movies and was used to obtain the regression equation ŷ = 0.145x + 0.136, where x represents the budget of a movie (in millions of dollars) and ŷ is the predicted score of that movie (in points from 0 to 1). What is the predicted score of a movie that has a $5 million budget?

0.861 points

An urban planner collects data on how park trails are used by residents. The planner looks at two trails: one that winds through an urban area and another in a suburban park. The table shows the number of users who walk, jog, or bike the trail.

0.3350

A movie production company was interested in the relationship between the budget to make a movie and how well that movie was received by the public. Information was collected on several movies and was used to obtain the regression equation ŷ = 0.145x + 0.136, where x represents the budget of a movie (in millions of dollars) and ŷ is the predicted score of that movie (in points from 0 to 1). What is the predicted score of a movie that has a $250,000 budget?

0.17225 points

For the soccer banquet, the players and their family members selected their favorite main dish and side dish. Of the 39 people who chose chicken as the main dish, 18 wanted potatoes. Of the 32 people who chose rice as a side dish, 6 chose fish as a main dish. A total of 8 people chose a vegetarian meal with potatoes, and a total of 10 people chose fish as their main dish. Which two-way table correctly displays this data?

B

Victoria created the scatterplot below based on the data in the table for the ages and heights of some teachers in her school. Teacher Age vs. Height Teacher Age Height (in.) 1 36 62 2 28 70 3 50 60 4 44 72 5 58 68 6 24 65 She wants to see if a teacher's height depends on his or her age. What did she do wrong when she created the scatterplot?

She mixed up the x- and y-coordinates of the point representing teacher 3.

The Bureau of Labor Statistics is an office within the US Department of Labor. Every three months the bureau releases a report containing jobs and salary data of US workers. One statistic reported is the median weekly salary for full-time workers. The scatterplot shows the growth of median weekly salary, starting in January 2010. An equation of the least-squares for the data in the scatterplot is , where 2010 represents year zero. The value of r for the scatterplot is 0.977. Based on the least-squares regression and residual plot, is a linear model suitable for this data set?

A linear model is not suitable because the residual plot shows a clear pattern.

One method used to measure the speed of supercomputers is the number of floating-point mathematical operations the computer can perform in one second. This is often referred to by the acronym FLOPS. For many years since 1992, the number of FLOPS performed by the largest supercomputer available that year was recorded, and the natural log of each value of the response variable taken. Based on the scatterplot and computer output, a reasonable estimate for the number of computations performed per second by the largest supercomputer in 2007 is:

580,473 billion FLOPS because and e13.2716= 580,473.

Mr. Capuano, an art teacher, surveyed his students to find out whether they are satisfied with his classes. He also noted which class each student had taken. Oil-painting Satisfied: 17Not satisfied: 3 Sculpture Satisfied: 25Not satisfied: 5 What is the value of x in the relative frequency table for the survey results? Round the answer to the nearest percent.

6%

A survey was taken of children between the ages of 10 and 17 about how many siblings they have and whether they have a pet. The results of the survey are shown in the table. Which statement must be true?

Out of the 97 children who have 1 sibling, 40 of them do not have a pet.

An economist studies the relationship between the unemployment rate of adult males and male life expectancy for 12 European countries. The relationship is shown in the scatterplot. The value of r for the scatterplot is -0.423. Which statement best explains the relationship between the variables in the scatterplot?

Higher unemployment rates may have an association with unhealthy lifestyles, which is also associated with lower life expectancy.