
Concept explainers
a.
Find the explanatory variable and response variable to plot a
Find the direction, form and strength of the scatterplot.
a.

Answer to Problem 1E
Either weight in grams or weight in ounces could be the explanatory or response variable.
The association between the variables is straight, positive and strong.
Explanation of Solution
Given info:
The variables of the apples are given one is weight in grams and the other is weight in ounces.
Justification:
Associated variables:
Two variables are associated or related if the value of one variable gives you information about the value of the other variable.
The two variables weight in grams and weight in ounces are associated variables.
Response variable:
The variable to be measured or observed in
Therefore, the dependent variables which is measured by the independent variables is called the response variable.
Here, given two variables are weight in grams of apple and weight in ounces of apple.
That is, each apple’s weight is measured in two different scales.
Therefore, there will be chances for weight in grams to depend on weight in ounces and vice versa.
Thus, either weight in grams or weight in ounces could be the explanatory or response variable.
Explanatory variable:
The variable used to predict or explain the response variable is called as predictor variable or explanatory variable. In other words it can also be defined as, the variable that explains the changes in the response variable is defined as explanatory variable.
Therefore, the independent variables to predict the response variable is called the predictor variable.
Here, given two variables are weight in grams of apple and weight in ounces of apple.
That is, each apple’s weight is measured in two different scales.
Therefore, there will be chances for weight in grams to depend on weight in ounces and vice versa.
Thus, either weight in grams or weight in ounces could be the explanatory or response variable.
Form of the association between variable:
The form of the association describes whether the data points follow a linear pattern or some other complicated curves. For data if it appears that a line would do a reasonable job of summarizing the overall pattern in the data. Then, the association between two variables is linear.
Here, weight in ounces increases or decreases with the increase or decrease in the weight in grams.
The pattern of the relationship between weight in ounces and weight in grams represents a straight line.
Hence, the association between the weight in ounces and weight in grams is linear.
Direction of association:
If the increase in the values of one variable increases the values of another variable, then the direction is positive. If the increase in the values of one variable decreases the values of another variable, then the direction is negative.
Here, weight in ounces increases or decreases with the increase or decrease in the weight in grams.
Hence, the direction of the association is positive.
Strength of the association:
The association is said to be strong if all the points are close to the straight line. It is said to be weak if all points are far away from the straight line and it is said to be moderate if the data points are moderately close to straight line.
Here, the variables will have perfect
Hence, the association between the variables is strong.
b.
Find the explanatory variable and response variable to plot a scatterplot.
Find the direction, form and strength of the scatterplot.
b.

Answer to Problem 1E
Circumference of apple is explanatory variable and weight is the response variable.
The association between the variables is straight, positive and strong.
Explanation of Solution
Given info:
The variables of the apples are given one is circumference in inches and the other is weight in ounces.
Justification:
Associated variables:
Two variables are associated or related if the value of one variable gives you information about the value of the other variable.
The two variables circumference in inches and weight in ounces are associated variables.
Response variable:
The variable to be measured or observed in regression analysis is called as response variable. In other words it can also be defined as, the variable that is changed due to the impact of the explanatory variable is defined as response variable.
Therefore, the dependent variables which is measured by the independent variables is called the response variable.
Here, given two variables are circumference in inches of apple and weight in ounces of apple.
Three dimensional volume is nothing but the weight and one dimensional circumference explains the three dimensional volume.
Therefore, weight of the apple is predicted with the circumference of the apple.
That is, weight of the apple is depend on the circumference of the apple.
Thus, weight in ounces is dependent or response variable.
Explanatory variable:
The variable used to predict or explain the response variable is called as predictor variable or explanatory variable. In other words it can also be defined as, the variable that explains the changes in the response variable is defined as explanatory variable.
Therefore, the independent variables to predict the response variable is called the predictor variable.
Here, given two variables are circumference in inches of apple and weight in ounces of apple.
Weight of the apple is predicted with the circumference of the apple.
Thus, circumference in inches is independent or explanatory variable.
Form of the association between variable:
The form of the association describes whether the data points follow a linear pattern or some other complicated curves. For data if it appears that a line would do a reasonable job of summarizing the overall pattern in the data. Then, the association between two variables is linear.
Here, weight in ounces increases or decreases with the increase or decrease in the circumference in inches of apple.
The pattern of the relationship between weight in ounces and circumference in inches of apple represents a straight line for same size apples.
Hence, the association between the weight in ounces and circumference in inches of apple is linear for same size apples.
The association curve will be apparent if the sample contains very large and very small apples.
Direction of association:
If the increase in the values of one variable increases the values of another variable, then the direction is positive. If the increase in the values of one variable decreases the values of another variable, then the direction is negative.
Here, weight in ounces increases or decreases with the increase or decrease in the circumference in inches of apple.
Hence, the direction of the association is positive.
Strength of the association:
The association is said to be strong if all the points are close to the straight line. It is said to be weak if all points are far away from the straight line and it is said to be moderate if the data points are moderately close to straight line.
Here, the variables will have perfect correlation between them.
Hence, the association between the variables is strong.
c.
Find the explanatory variable and response variable to plot a scatterplot.
Find the direction, form and strength of the scatterplot.
c.

Answer to Problem 1E
The variables shoe size and grade point average are not associated with each other.
Explanation of Solution
Given info:
The variables of the college freshmen are given one is shoe size and the other is grade point average.
Justification:
Associated variables:
Two variables are associated or related if the value of one variable gives you information about the value of the other variable.
There is no relationship between the variables shoe size and grade point average.
Therefore, there is no association between the variables.
Hence, the discussion will not go further.
d.
Find the explanatory variable and response variable to plot a scatterplot.
Find the direction, form and strength of the scatterplot.
d.

Answer to Problem 1E
Circumference of apple is explanatory variable and weight is the response variable.
The association between the variables is straight, negative and strong.
Explanation of Solution
Given info:
The variables of the gasoline are given one is number of miles drove since filling up and the other is gallons remaining in the tank.
Justification:
Associated variables:
Two variables are associated or related if the value of one variable gives you information about the value of the other variable.
The two variables number of miles drove since filling up and gallons remaining in the tank are associated variables.
Response variable:
The variable to be measured or observed in regression analysis is called as response variable. In other words it can also be defined as, the variable that is changed due to the impact of the explanatory variable is defined as response variable.
Therefore, the dependent variables which is measured by the independent variables is called the response variable.
Here, given two variables are number of miles drove since filling up and gallons remaining in the tank.
The fuel that is remained in the tank is dependent on the fuel that is used for driving.
Therefore, gallons remaining in the tank is predicted with the number of miles drove since filling up.
That is, gallons remaining in the tank is depend on the number of miles drove since filling up.
Thus, gallons remaining in the tank is dependent or response variable.
Explanatory variable:
The variable used to predict or explain the response variable is called as predictor variable or explanatory variable. In other words it can also be defined as, the variable that explains the changes in the response variable is defined as explanatory variable.
Therefore, the independent variables to predict the response variable is called the predictor variable.
Here, given two variables are number of miles drove since filling up and gallons remaining in the tank.
Gallons remaining in the tank is predicted with the number of miles drove since filling up.
Thus, the number of miles drove since filling up is independent or explanatory variable.
Form of the association between variable:
The form of the association describes whether the data points follow a linear pattern or some other complicated curves. For data if it appears that a line would do a reasonable job of summarizing the overall pattern in the data. Then, the association between two variables is linear.
Here, gallons remaining in the tank decreases with the increase in the number of miles drove since filling up.
The pattern of the relationship between gallons remaining in the tank and the number of miles drove since filling up represents a straight line.
Hence, the association between the gallons remaining in the tank and the number of miles drove since filling up is linear.
Direction of association:
If the increase in the values of one variable increases the values of another variable, then the direction is positive. If the increase in the values of one variable decreases the values of another variable, then the direction is negative.
Here, gallons remaining in the tank decreases with the increase in the number of miles drove since filling up and gallons remaining in the tank increases with the decrease in the number of miles drove since filling up.
Hence, the direction of the association is negative.
Strength of the association:
The association is said to be strong if all the points are close to the straight line. It is said to be weak if all points are far away from the straight line and it is said to be moderate if the data points are moderately close to straight line.
Here, the variables will have moderate correlation between them.
Hence, the association between the variables is moderate.
Want to see more full solutions like this?
Chapter 6 Solutions
STATS:DATA+MODELS-W/DVD
- Suppose the Internal Revenue Service reported that the mean tax refund for the year 2022 was $3401. Assume the standard deviation is $82.5 and that the amounts refunded follow a normal probability distribution. Solve the following three parts? (For the answer to question 14, 15, and 16, start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined. 1.What percent of the refunds are more than $3,500? 2. What percent of the refunds are more than $3500 but less than $3579? 3. What percent of the refunds are more than $3325 but less than $3579?arrow_forwardA normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts? 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the answer of the second part.) 2. Compute the probability of a value greater than 55.0. Use the same formula, x=55 and subtract the answer from 1. 3. Compute the probability of a value between 52.0 and 55.0. (The question requires finding probability value between 52 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 52, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…arrow_forwardIf a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24? The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by a step by step creating a chart. Clearly mark the range, identifying the…arrow_forward
- Client 1 Weight before diet (pounds) Weight after diet (pounds) 128 120 2 131 123 3 140 141 4 178 170 5 121 118 6 136 136 7 118 121 8 136 127arrow_forwardClient 1 Weight before diet (pounds) Weight after diet (pounds) 128 120 2 131 123 3 140 141 4 178 170 5 121 118 6 136 136 7 118 121 8 136 127 a) Determine the mean change in patient weight from before to after the diet (after – before). What is the 95% confidence interval of this mean difference?arrow_forwardIn order to find probability, you can use this formula in Microsoft Excel: The best way to understand and solve these problems is by first drawing a bell curve and marking key points such as x, the mean, and the areas of interest. Once marked on the bell curve, figure out what calculations are needed to find the area of interest. =NORM.DIST(x, Mean, Standard Dev., TRUE). When the question mentions “greater than” you may have to subtract your answer from 1. When the question mentions “between (two values)”, you need to do separate calculation for both values and then subtract their results to get the answer. 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…arrow_forward
- If a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24? The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by creating a chart. Clearly mark the range, identifying the lower and upper…arrow_forwardProblem 1: The mean hourly pay of an American Airlines flight attendant is normally distributed with a mean of 40 per hour and a standard deviation of 3.00 per hour. What is the probability that the hourly pay of a randomly selected flight attendant is: Between the mean and $45 per hour? More than $45 per hour? Less than $32 per hour? Problem 2: The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds. What is the area between 415 pounds and the mean of 400 pounds? What is the area between the mean and 395 pounds? What is the probability of randomly selecting a value less than 395 pounds? Problem 3: In New York State, the mean salary for high school teachers in 2022 was 81,410 with a standard deviation of 9,500. Only Alaska’s mean salary was higher. Assume New York’s state salaries follow a normal distribution. What percent of New York State high school teachers earn between 70,000 and 75,000? What percent of New York State high school…arrow_forwardPls help asaparrow_forward
- Solve the following LP problem using the Extreme Point Theorem: Subject to: Maximize Z-6+4y 2+y≤8 2x + y ≤10 2,y20 Solve it using the graphical method. Guidelines for preparation for the teacher's questions: Understand the basics of Linear Programming (LP) 1. Know how to formulate an LP model. 2. Be able to identify decision variables, objective functions, and constraints. Be comfortable with graphical solutions 3. Know how to plot feasible regions and find extreme points. 4. Understand how constraints affect the solution space. Understand the Extreme Point Theorem 5. Know why solutions always occur at extreme points. 6. Be able to explain how optimization changes with different constraints. Think about real-world implications 7. Consider how removing or modifying constraints affects the solution. 8. Be prepared to explain why LP problems are used in business, economics, and operations research.arrow_forwardged the variance for group 1) Different groups of male stalk-eyed flies were raised on different diets: a high nutrient corn diet vs. a low nutrient cotton wool diet. Investigators wanted to see if diet quality influenced eye-stalk length. They obtained the following data: d Diet Sample Mean Eye-stalk Length Variance in Eye-stalk d size, n (mm) Length (mm²) Corn (group 1) 21 2.05 0.0558 Cotton (group 2) 24 1.54 0.0812 =205-1.54-05T a) Construct a 95% confidence interval for the difference in mean eye-stalk length between the two diets (e.g., use group 1 - group 2).arrow_forwardAn article in Business Week discussed the large spread between the federal funds rate and the average credit card rate. The table below is a frequency distribution of the credit card rate charged by the top 100 issuers. Credit Card Rates Credit Card Rate Frequency 18% -23% 19 17% -17.9% 16 16% -16.9% 31 15% -15.9% 26 14% -14.9% Copy Data 8 Step 1 of 2: Calculate the average credit card rate charged by the top 100 issuers based on the frequency distribution. Round your answer to two decimal places.arrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman





