Test 1

A study of the behavior of a large number of drug offenders after treatment for drug abuse suggests that the likelihood of conviction within a two year period after treatment may depend on the offender's education. The proportion of the total number of cases that fall into the four education/conviction categories are shown below: Status within 2 years After treatment Education Convicted Not convicted Totals 10 Years or more 0.1 0.3 0.4 9years or less 0.27 0.33 0.6 Totals 0.37 0.63 1 Suppose a single offender is selected from the treatment program. Here are the events of interest:A: The offender has 9 or less years of educationB: The offender is convicted within 2 years after completion of treatment. Find P(A intersect B).

. 0.27

Students in a stat class are given this set of data: 5716, 5944, 4764, 1750, 3811, 1940, 5650, 7982, 5203, 9393, 3256 and are asked to construct the stem and leaf plot. The instructor, when grading, only looks at the first digits of each piece of data. Which student is on the right track?

. 1 | 7 9 2 |

Scores on a test in a very large class are bell-shaped and symmetric. The mean on the test was 75, and the standard deviation was 5. What percent of the scores were above 80?

. 16%

If a value X is the 60th percentile of a data distribution, which of the following statements is true?

. 60% of the data fall below X

What type of graph is appropriate for qualitative data?

. Bar graph

In a study on the effectiveness of 2 pain medications, 100 patients (50 taking each type of medication) were asked to record the level of pain on a scale of 1-10 each morning when they awoke. They did this for 7 days while taking each medication. What is the experimental unit of this study?

. Each patient

A statistician, Professor Jones, hires an intern to help with some analyses over the summer. The intern provides a report showing a correlation of r = 2.52 between two variables x and y. What should Professor Jones conclude immediately?

. There is a high outlier in the data causing the r value to be quite high.

A movie critic group's website rates movies on a scale of 0 to 100. The site provides a rating based on the published reviews of movie critics and also provides a rating based on audience surveys. The critics' rating and audience score for all movies release in 2020 were used to produce the scatterplot below, where the horizontal axis contains the movie critic group's score and the vertical axis contains the audience rating. Based on the scatterplot, which of the following would be closest to the value of the correlation coefficient for the movie critic group's and the audience rating?

0.8

The total miles traveled during the month of February in the United States for the years 1987 through 2012 was recorded. The given scatter plots summarize this data. What value is the best estimate of the correlation coefficient for the years 1987-2012?

0.958

The number of tuberculosis (TB) cases in Californian counties in the year 2019 was recorded. The given JMP applet shows various scatterplots of the number of TB cases versus the population of each of these counties in that year. What value below is the best estimate of the correlation between tuberculosis cases and population for all of the data (a population of 0 - 38,501,494 people)?

0.99

For the given set of data, −1, 2, 6, 8, 8, 2, 6, 4, −1, 8, 6, 6, what is the frequency of 4?

1

The data relating the square feet for the living space and the selling price of 12 residential properties given in example 3.5 are reproduced here. XY1360178.51940275.71750239.51550229.81790195.61750210.32230360.51600205.21450188.61870265.72210325.31480168.8 What is the y-intercept of the best fitting line?

1. -106.6

A random variable x has this probability distribution:x012345p(X)0.10.30.40.1?0.05 Find s

1. 1.19

An experiment consists of tossing a single die and observing the number of dots that show on the upper face. Events A, B, C are defined as follows:A: Observe a number less than 4B: Observe a number less than or equal to 2.C: Observe a number greater than 3. Find P(A intersect B).

1. 1/3

These data relate the amount spent on groceries per week and the numbers of household members are x y 2 45.75 2 60.19 3 68.33 4 100.92 1 35.86 5 130.62 What is the y-intercept of the best fitting line?

1. 6.1

The game of roulette uses a wheel containing 38 pockets. Thirty-six pockets are numbered 1,2...36, and the remaining two are marked 0 and 00. The wheel is spun, and a pocket is identified as winner. Assume that the observance of any one pocket is just as likely as any other. Suppose you placed bets on the number 1 through 18. What is the probability that one of the numbers is a winner?

1. 9/19

The manager of the cosmetics department in a women's store wished to assess the average wait time of customers waiting in line to make a purchase. The manager decided to ask 20 random customers in line for the length of wait time (in minutes) prior to purchase, and use the results to decide if an additional cashier should be placed in this department. Analyze the results in the histogram. How many customers waited in line 6 minutes or longer?

10 customers

Professor Issac Asimov was one of the prolific writers of all time. He wrote nearly 500 books during a 40year career prior to death in 1992. In fact, as his career progressed, he became even more productive in terms of the number of books written within a given period of time. These data are times required to write his books, In increments of 100s. Number of books (y) 100 200 300 400 490Time in months (x) 237 350 419 465 507 The relationship between the two variables appears to be nonlinear.

2. False

Identify the following as discrete or continuous random variables:Shelf life of a particular drug.

2. Continuous

When do creative people get their best ideas? USA Today did a survey of inventors (who hold U.S. patents) and obtained the following information. Find the probability that a creative inventor got his/her best idea during the 12 midnight - a.m. time frame.

222/966

In a sales effectiveness seminar, a group of sales representatives tried two approaches to selling a new automobile to a customer: the aggressive approach and the passive approach. For customers, the following record was kept. Suppose a customer is selected at random from the 1160 total customers. Find the probability that a sale was made and that the sales approach was aggressive.

270/1160

During a special promotion at an electronics store, a customer purchasing a computer and printer is given a choice of 5 free software packages. There are 15 different software packages from which to select. How many different groups of software packages can be selected?

3,003 groups

Arches National Park is located in southern Utah. The park is famous for its beautiful desert landscape and its many natural sandstone arches. Park Rangers are currently conducting an inventory (not yet complete) of natural arches within the park that have an opening of at least 3 feet. The height of the arch opening is rounded to the nearest foot. Find the probability that a randomly chosen arch in the park will have an arch height of 50 - 74 feet.

33/288

An experiment consists of tossing a single die and observing the number of dots that show on the upper face. Events A, B, C are defined as follows:A: Observe a number less than 4B: Observe a number less than or equal to 2.C: Observe a number greater than 3.Find P(B intersect C).

4. 0

A random variable x has this probability distribution:x012345p(X)0.10.30.40.1?0.05 Find s2

4. 1.43

The University of Montana ski team has five entrants in a men's downhill ski event. The coach would like the first, second, and third places to go to the team members. In how many ways can the five team entrants achieve first, second, and third places?

60 ways

There are three nursing positions to be filled at Lilly Hospital. Position 1 is the day nursing supervisor; position 2 is the night nursing supervisor; and position 3 is the nursing coordinator position. There are 10 candidates qualified for all three of the positions. Find the number of different ways the positions can be filled by these applicants?

720 ways

A class of 40 students, aged 12, was measured for weight and height. The results are summarized and the equation of the trendline is y = 0.448x + 58.2, where the variable "x" represents student height (in inches) the variable "y" represents the student weight in pounds. What is the predicted weight for a child that is 65 inches tall? (Round your answer to the nearest integer.)

87 lbs.

Henry scored 82, 73, 84, and 68 on four exams. What must he make on the fifth exam to have a mean average of 80?

93

Arches National Park is located in southern Utah. The park is famous for its beautiful desert landscape and its many natural sandstone arches. Park Rangers are currently conducting an inventory (not yet complete) of natural arches within the park that have an opening of at least 3 feet. The height of the arch opening is rounded to the nearest foot. Find the probability that a randomly chosen arch in the park will have an arch height of 10 - 29 feet.

96/288

In Excel, if the formula =A4-$B$11 is copied one row down, what is the result?

=A5-$B$11

In an Excel spreadsheet, a set of data is stored in ascending order in cells A1, A2, A3, ..., A18. Write an Excel formula that would calculate the median of this set of data.

=MEDIAN is (A1:A18)

A set of bivariate data has a correlation coefficient of 0.13. Interpret the meaning of this value.

A weak relationship exists between the two variables. As the value of the first variable increases, the value of the second variable increases.

What type of graph is appropriate for qualitative data?

Bar graph

What type of graph is appropriate for quantitative data?

Bar graph Histogram Pie chart

There are 50 qualified applicants for 10 trainee positions in a retail management program. Which calculation will how many different groups of trainees can be selected?

COMBIN(50,10)

SCUBA divers have maximum dive times they cannot exceed when going to different depths. The data in the table show different depths with the maximum dive times in minutes.

Can this model be used to predict the maximum dive time for a depth of 150 feet? c. No, because the model was not built for such depths.

The z-score closer to the value 0 means its most..

Common

Income, temperature, height, weight, and distance are all what kind of variables?

Continuous

Suppose that all 75 employees of a company received a raise of $150 per month? How would this affect the mean salary of all employees in this company?

D. The mean salary would increase by $150.

Number of books published or goals scored are an example of what kid of variable?

Discrete

Which of the following distributions is right-skewed?

Distribution 3

True or False: The Empirical Rule can be applied to any set of data

False

When using Excel's MEDIAN function, it is necessary to sort the data from least to greatest first.

False

SCUBA divers have maximum dive times they cannot exceed when going to different depths. The data in the table show different depths with the maximum dive times in minutes.

Find the least squares regression line and predict the maximum dive time for 85 feet. Maximum dive time is given in minutes, and assume that a linear model is appropriate even though it may not be. b. 32.5 minutes

What's the short cut for absolute value on excel?

Highlight the range and click fn+f4

Which of the following data sets will have a standard deviation of 0? I. 0,0,0,0,0 II. 5,5,5,5,5,5 III.-5,-5,0,5,5,

I and II If the numbers are the same Standard D is 0

The total miles traveled during the month of February in the United States for the years 1987 through 2012 was recorded. The given scatter plots summarize this data. What can be said about the relationship between the number of miles traveled in February and between the years 1987 and 2012?

In general, as the year increases, the number of miles traveled in February increases.

On which of the following would a single low outlier have a direct impact?

MeanRangeStandard D

The following scatterplot contains information on 133 movies released in 2020. Data on domestic gross (the income from the film in the U.S. in millions of dollars), production budget (in millions of dollars), and movie genre (action, adventure, etc.) were considered. Did the movie with the highest production budget also have the highest domestic gross?

No

Consider the following events for a driver selected at random from the general population.A = driver is under 25 years old. B = driver has received a speeding ticket in the last year. Translate "The probability the driver has received a speeding ticket in the last year and is under 25 years old" into symbols.

P(A and B)

Taking the range of a data set and dividing by 4 is a reliable estimate of what?

Standard deviation

Data on the prevalence of smoking in adults in California between the years 1984 and 2013 was collected. When comparing the percentages of smokers over time, caution must be used since the definition of "current smoker" was broadened in 1996, and then in 2012 the survey methods changed. The given scatterplots summarize the data. How did the change in the definition of "current smoker" affect the correlation coefficient? Compare the years 1984-1995 to the years 1996-2013.

The change in the definition of "current smoker" caused the correlation coefficient to become stronger

SCUBA divers have maximum dive times they cannot exceed when going to different depths. The data in the table and the scatterplot show different depths with the maximum dive times in minutes.

The correlation between x and y is -0.963, so is a linear model appropriate? No, because the scatterplot indicates a curved pattern to the relationship. A different model should really be used.

Servers at a restaurant want to know if there is a relationship between the amount they are given in tips and the cost of the meal. Data was collected and summarized in the scatterplot. One person paid a bill of $15.73 and tipped $5.00. Based on the scatterplot, what conclusion can be drawn?

The server was given a generous tip.

Servers at a restaurant want to know if there is a relationship between the amount they are given in tips and the cost of the meal. Data was collected and summarized in the scatterplot. As the value of the bill amount increases, what happens to the tip amount?

The tip amount increases.

An r-value close to zero indicates what?

There could be a strong relationship between y and x, but if so, it is not linear.

A class of 40 students, aged 12, was measured for weight and height. The results are summarized in the scatterplot. The equation of the trendline is y = 0.448x + 58.2, where the variable "x" represents student height (in inches) the variable "y" represents the student weight in pounds. Based on the scatterplot, what conclusion can be made regarding the relationship of height and weight of 12-year-old students in this class?

There is a moderately strong positive linear relationship between a student's height and weight.

Discrete variables cannot be a decimal. True or false

True

True or False: For a linear association, the sign (positive or negative) of r will be the same as that of the slope b.

True

The z-score further from the value 0 means its most

Unusual

Given the stem and leaf plot, where the stem is the ten's place and the leaf is the one's place.

What is the 10th largest data value? :c. 35

Amelia plays basketball for her high school. She wants to improve to play at the college level. She notices that the number of points she scores in a game goes up in response to the number of hours she practices her jump shot each week. She records the following data:

What is the r-value when relating the number of hours practiced and the number of points scored? d. 0.998

Amelia plays basketball for her high school. She wants to improve to play at the college level. She notices that the number of points she scores in a game goes up in response to the number of hours she practices her jump shot each week. She records the following data:

What is the slope of the regression line relating the number of hours practiced and the number of points scored? e. 2.971

Amelia plays basketball for her high school. She wants to improve to play at the college level. She notices that the number of points she scores in a game goes up in response to the number of hours she practices her jump shot each week. She records the following data:

What is the y-intercept of the regression line relating the number of hours practiced and the number of points scored? c. 0.765

The data listed here are the weights (in pounds) of 27 packagesOf ground beef in a supermarket meat display: 1.080.870.990.890.970.891.180.961.411.121.281.120.830.931.061.241.140.891.380.980.751.140.960.921.081.18 1.17 Find the upper quartile

a. 1.17

Given the following sample data set: 8, 7, 1, 4, 6, 6, 4, 5, 7, 6, 3, 0. Calculate the z-score for the largest observation.

a. 1.32

Scores on a test in a very large class are bell-shaped and symmetric. The mean on the test was 75, and the standard deviation was 5. What percent of the scores were below 65?

a. 2.5%

In an Excel spreadsheet, a set of numbers is stored in cells B1, B2, B3, , B9. Write an Excel formula that would calculate the lower quartile of this data.

a. =QUARTILE(B1:B9,1)

Which of the following is not a valid type of data?

a. Qualitative continuous

The 68-95-99.7 rule is formally known as:

a. The Empirical Rule

A random sample from an unknown population had a sample standard deviation of zero. Which statement is reasonable conclusion?

a. The sample range must be zero.

Which of the following best describes measures of center?

a. They are numbers around which observations tend to cluster and that describe the location of what in some sense might be called the "center" of a data set

Complete the sentence: Any subset of the sample space is called _____.

a. an event

Complete the sentence: In a histogram, the proportion of the total area which must be to the left of the median is _____.

a. exactly 0.50

When a customer enters a grocery store, there are three simple events: buy nothing, buy a small amount of items, or buy a large amount of items. In this situation, if the customer buys a small amount of items, then the customer cannot also buy a large amount of items. Which best describes these three simple events?

a. mutually exclusive

Complete the sentence: If two data sets have the same range, then _____.

a. the distances from the smallest to largest observations in both sets will be the same

What percent of data values fall within 1 standard deviation of the mean, according to the Empirical Rule?

approximately 68%

What percent of data values fall within 3 standard deviation of the mean, according to the Empirical Rule?

approximately 97.5

Given the following sample data set: 8, 7, 1, 4, 6, 6, 4, 5, 7, 6, 3, 0. Calculate the z-score for the smallest observation.

b. -1.94

Given the following sample data set: 8, 7, 1, 4, 6, 6, 4, 5, 7, 6, 3, 0. Use the Excel function, QUARTILE to find the lower quartile.

b. 3.75

Arrange the graphs from the lowest r value to highest r value.

b. 4, 2, 6, 5, 3, 1

In the set of data: 0, 4, 4, 6, 7, 8, 10, 11, 11, 12, 12, 13, use Excel's QUARTILE function to find Q1.

b. 5.5

In Excel, if the formula =A4-$B$11 is copied one row down, what is the result?

b. =A5-$B$11

A random sample of 11 statistics students produced data where x is the third exam score out of 80, and y is the final exam score out of 200. The corresponding regression line has the equation: y = -173.51 + 4.83x, and the value of r2 (the "coefficient of determination") is found to be 0.44. What is the proper interpretation of r2?

b. About 44% of the variation in the final exam score can be explained by the students' scores on the 3rd exam. The remaining 56% is due to other factors or unexplained randomness.

What percent of data values fall within 1 standard deviation of the mean, according to the Empirical Rule?

b. Approximately 68%

Typically, "countable" variables are:

b. Discrete

Which of the following is a quantitative continuous variable?

b. Distance a family travels on vacation

5 students are observed. The color of each of their backpacks is recorded. One student has a red backpack, two students have blackpacks, one student has a green backpack, and one has a gray backpack. TRUE or FALSE: Quantitative data were measured

b. False

Given the following sample data set: 8, 7, 1, 4, 6, 6, 4, 5, 7, 6, 3, 0. The z-score for the largest observation Is unusually large

b. False

True or False? When two variables appear to be highly correlated, we may infer that there is a cause and effect relationship present

b. False

Which of the following statements about the mean is NOT always correct?

b. Half of the observations are on either side of the mean.

What is meant by the "Five Number Summary"?

b. Minimum, Q1, median, Q3, Maximum

The number of floors of each of 40 buildings in a particular city is recorded. Make a stem-and-leaf plot of the data. (You should be able to eliminate choices fairly quickly without manually checking every single leaf).

b. Plot b

Which of the following are measures of spread?

b. Range

Ethan repairs household appliances like dishwashers and refrigerators. For each visit, he charges $25 plus $20 per hour of work. A linear equation that expresses the total amount of money Ethan earns per visit is y = 25 + 20x. What is the slope and y-intercept of the linear model?

b. Slope = 20; y-intercept = 25

A TV consumer reporter is recording the number of free classes (kickboxing, cycling, etc.) offered at each of the different gyms throughout the city. What are the "experimental units" in this situation?

b. The gyms

A law school administrator was interested in whether a student's score on the entrance exam can be used to predict a student's grade point average (GPA) after one year of law school. The administrator studied 15 students. It was shown that the correlation between the entrance exam score and the grade point average after one year of law school was 0.934. Based on this information, interpret the correlation coefficient.

b. The higher a student's entrance exam score, the higher his GPA after one year of law school.

For the dotplot shown below, which of the following is true?

b. The mean is higher than the median

A football coach wants to determine the relationship between the number of rushing yards and the number of passing yards by the quarterbacks on the team per game. If he plots the number of rushing yards as a function of the number of passing yards, how is is graph set up?

b. The number of passing yards is the x variable (horizontal) and the number of rushing yards is the y variable (vertical).

Given the five number summary: 5, 12, 15, 16, 20, are there any outliers in the data? (use the rule involving these numbers)

b. There is at least one low outlier.

Complete the sentence: A scatterplot can be used to determine the relationship between _____.

b. two quantitative variables

A manufacturing firm producing odd-sized, decorative windows buys the window frames from either supplier S1 or supplier S2. The firm sells the finished window to either customer C1 or customer C2. Describe the sample space; the list of all possible supplier-customer combinations, which a finished window might represent.

b. {(C1, S1), (C1, S2), (C2, S1), (C2, S2)}

A distribution of measurements is relatively mound-shapedwith mean 50 and standard deviation 10. If a measurement is chosen at random from this distribution, what is the probability that it will be greater than 60?

b. 0.16

Given the following sample data set:3, 9, 10, 2, 6, 7, 5, 8, 6, 6, 4, 9, 22 Calculate the z-score for the smallest observation.

c. -1.10

Given the following sample data set:3, 9, 10, 2, 6, 7, 5, 8, 6, 6, 4, 9, 22 Find the upper quartile

c. 9

The manager of a video store was interested in examining the relationship between a person's weekly take-home pay and the number of movies rented by that person per week. He polled 50 customers. In an Excel spreadsheet, the take-home pays of the 50 customers are stored in cells A1 to A50, and the number of videos rented per week by the 50 customers are stored in cells B1 to B50. Write an Excel formula that will find the correlation coefficient of this data.

c. =CORREL(A1:A50,B1:B50)

In professional sports, many minor-league or rookie players earn relatively low salaries, while a few more experienced players and even fewer "superstars" earn high salaries. The distribution of such salaries is likely:

c. Right-skewed

Which of the following is a disadvantage of using the sample range to measure spread or dispersion?

c. The largest or smallest observation (or both) may be an outlier

An r-value close to zero indicates what?

c. There could be a strong relationship between y and x, but if so, it is not linear.

Which measure of center is meaningful when the data are qualitative?

c. mode

In Excel, which of the following is an "absolute" cell reference?

d. $A$10

A distribution of measurements is relatively mound-shaped with mean 50 and standard deviation 10. What proportion of the measurements will fall between 30 and 60?

d. 0.81

The data listed here are the weights (in pounds) of 27 packages Of ground beef in a supermarket meat display: 1.080.870.990.890.970.891.180.961.411.121.281.120.830.931.061.241.140.891.380.980.751.140.960.921.081.18 1.17 Find the percentage of measurements in the interval x-bar ± 3s.

d. 100%

On which of the following would a single low outlier have a direct impact?

d. All of these

What type of graph is appropriate for quantitative data?

d. All of these

Order the following from being the most common to the most unusual: A: having a z-score near 5 B: having a z-score near -2 C: having a z-score near 0 D: having a z-score near 0.8

d. C, D, B, A

A random sample of 11 statistics students produced data where x is the third exam score out of 80, and y is the final exam score out of 200. The corresponding regression line has the equation: y = -173.51 + 4.83x. What is the proper interpretation of the numerical value of the slope?

d. For each 1 point increase in the third exam score, we expect the final exam score to increase by 4.83 points.

A manager of a grocery store wishes to show the relationship between the number of customers who come to the store on the weekends, and the total sales volume (in dollars) during the same weekend. The manager has 52 weeks of this data. Which type of graph would be most useful?

d. Scatterplot

Ethan repairs household appliances like dishwashers and refrigerators. For each visit, he charges $25 plus $20 per hour of work. A linear equation that expresses the total amount of money Ethan earns per visit is y = 25 + 20x. What is the independent variable, and what is the dependent variable?

d. The independent variable is the number of hours, the dependent variable is his total charge for each visit.

When the price of gasoline becomes too high, consumers become very concerned about the gas mileage obtained by their vehicles. One consumer was interested in the relationship between a vehicle's engine size (in cylinder) and gas mileage (measured in miles per gallon). The consumer gathered data from 7 vehicle owners. It was shown that the correlation between the engine size and gas mileage was -0.371. Based on this information, interpret the correlation coefficient.

d. There is not a relationship between the size of an engine and the vehicle's gas mileage.

Which of the following randomly selected measurements, x, might be considered a potential outlier if it was selected from the given population?

d. x = 4 from a population with mean = 0 and standard deviation = 1.

On which of the following would a single high outlier have a direct impact?

e. None of these

Taking the range of a data set and dividing by 4 is a reliable estimate of what?

e. Standard deviation

Which of the following scatterplots have an r value close to zero?

f. All of these have an r close to 0.

Scores on a test in a very large class are bell-shaped and symmetric. The mean on the test was 75, and the standard deviation was 5. What percent of the scores were above 75?

g. 50%

Scores on a test in a very large class are bell-shaped and symmetric. The mean on the test was 75, and the standard deviation was 5. What percent of the scores were between 65 and 85?

j. 95%

A variable, x, represents the name of the university where a student is enrolled. What type of variable is the variable x?

qualitative

A movie critic group's website rates movies on a scale of 0 to 100. The site provides a rating based on the published reviews of movie critics and also provides a rating based on audience surveys. The critics' rating and audience score for all movies release in 2020 were used to produce the scatterplot below, where the horizontal axis contains the movie critic group's score and the vertical axis contains the audience rating. Based on the scatterplot, which of the following best describes the relationship between the movie critic group's score and the audience rating?

strong positive linear relationship