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elementary statistics

Questions and Answers of Elementary Statistics

After learning his score on a recent statistics exam, Ed bragged to his friends: ‘‘My score is the first quartile of the class.’’ Did Ed have a good reason to brag? Explain.
On a final exam in a large statistics class, Tom’s score was the tenth percentile, Dick’s was the median, and Harry’s was the third quartile. Which of the three scores was the highest? Which
In 2016, the Chicago Cubs defeated the Cleveland Indians to become the champions of Major League Baseball. Following are the salaries, in millions of dollars, of the players on each of these teams.a.
Following are levels of particulate emissions for 65 vehicles driven at sea level, and for 35 vehicles driven at high altitude.a. Find the median, the first quartile, and the third quartile of the
Following are boxplots of the level of fine particle air pollution, in micrograms per cubic meter, in the cities of Denver and Greeley, Colorado, during a recent winter.a. In which city is the
Following are boxplots of diastolic blood pressure, in millimeters, for a sample of people aged 18–39 years, and a sample over 60 years old. The data are consistent with results reported by the
The most recent United States Census reported the per capita incomes for each of the 50 states.The five-number summary, in thousands of dollars, is Minimum: 20.0, Q1: 24.1, Median: 25.7, Q3: 29.0,
Following is the five-number summary for the populations, in millions, for the 50 states of the United States.Minimum: 0.58, Q1: 1.86, Median: 4.49, Q3: 6.90, Maximum: 38.04a. Does the five-number
Ten residents of a town were asked how many children they had. The responses were as follows.a. Explain why the median and first quartile are the same.b. Construct a boxplot for these data.c. Explain
Make up a list of numbers whose boxplot has no whiskers.
Make up a data set in which the mean is greater than the third quartile.
Make up a data set in which the mean is less than the first quartile.
Seven families live on a small street in a certain town. Their annual incomes (in $1000s) are 15, 20, 30, 35, 50, 60, and 150.a. Find the first and third quartiles, and the IQR.b. Show that 150 is an
If we divide a data set into four approximately equal parts, the three dividing points are called quartiles. If we divide a data set into 100 approximately equal parts, the 99 dividing points are
Table 3.9 presents the February rainfalls in Los Angeles for the period 1972–2016.a. Show that the mean of these data is μ = 3.624 and the population standard deviation is σ = 3.410.b. Show that
Of the mean, median, and mode, which must be a value that actually appears in the data set?
The prices (in dollars) for a sample of personal computers are: 550, 700, 420, 580, 550, 450, 690, 390, 350.Calculate the mean, median, and mode for this sample.
If a computer with a price of $2000 were added to the list in Exercise 2, which would be affected more, the mean or the median?
In general, a histogram is skewed to the left if the__________________ is noticeably less than the ___________________ .
A sample of 100 students was asked how many hours per week they spent studying. The following frequency table shows the results:a. Approximate the mean time this sample of students spent studying.b.
A sample has a variance of 16.What is the standard deviation?
Each of the following histograms represents a data set with mean 20.One has a standard deviation of 3.96 and the other has a standard deviation of 2.28. Which is which? Fill in the blanks: Histogram
Assume that the histogram of starting salaries is approximately bell-shaped. Approximately what percentage of the salaries will be between \($34,680\) and $40,280?In Exercises 8–11, suppose that
Assume it is not known whether the histogram of starting salaries is bell-shaped. Fill in the blank: At least percent of the salaries will be between \($34,680\) and $40,280.In Exercises 8–11,
John’s starting salary is \($38,180\). What is the z-score of his salary?In Exercises 8–11, suppose that the mean starting salary of social workers in a specific region is \($37,480\) with a
Find the coefficient of variation of the salaries.In Exercises 8–11, suppose that the mean starting salary of social workers in a specific region is \($37,480\) with a standard deviation of $1,400.
True or false: If a student’s exam grade is on the 55th percentile, then approximately 45% of the scores are below his or her grade.In Exercises 8–11, suppose that the mean starting salary of
The five-number summary for a sample is 7, 18, 35, 62, 85.What is the IQR?In Exercises 8–11, suppose that the mean starting salary of social workers in a specific region is \($37,480\) with a
The prices (in dollars) for a sample of coffee makers are:19 22 29 68 35 37 28 22 41 39 28a. Find the first and third quartiles.b. Find the upper and lower outlier boundaries.c. Are there any
Construct a boxplot for the data in Exercise 14.Exercise 14 The prices (in dollars) for a sample of coffee makers are:19 22 29 68 35 37 28 22 41 39 28.In Exercises 8–11, suppose that the mean
Following are the annual amounts of federal support (in millions of dollars) for National Endowment for the Arts programs for the years 2010 through 2016.a. Find the mean annual amount of federal aid
The following table presents the profit, in a recent year, in billions of dollars, for each of the 15 largest U.S. corporations in terms of revenue.a. Find the mean profit.b. Find the median
A manufacturer of cell phone batteries determines that the average length of talk time for one of its batteries is 470 minutes. Suppose that the standard deviation is known to be 32 minutes and that
Using the data in Exercise 2:a. Find the first and third quartiles of the profit.b. Find the median profit.c. Find the upper and lower outlier boundaries.d. Are there any outliers? If so, list
Percentiles are values that divide a data set into hundredths. The values that divide a data set into tenths are called deciles, denoted D1,D2, ...,D9. Describe the relationship between percentiles
Electronic devices contain electric circuits etched into wafers made of silicon. These silicon wafers are sealed with an ultrathin layer of silicon dioxide, in a process known as oxidation. This can
Fill in the blank: If large values of one variable are associated with small values of another, then the two variables have a _______________________ association.
Fill in the blank: If two variables have a positive association, then large values of one variable are associated with __________________ values of the other.
Fill in the blank: If the points on a scatterplot tend to cluster around a straight line, the variables plotted have a ___________________ association.
For each of the following scatterplots, state the type of association that is exhibited:Choices: positive linear, negative linear, positive nonlinear, negative nonlinear, weak linear. b. d. e.
For each of the following pairs of variables, determine whether the association is positive or negative, and explain why.a. Would the association between outdoor temperature and consumption of
The National Assessment for Educational Progress (NAEP) is a U.S. government organization that assesses the performance of students and schools at all levels across the United States. The following
For which of the following scatterplots is the correlation coefficient an appropriate summary? (a) (b) (c)
An economist discovers that over the past several years, both the salaries of U.S.college professors and the amount of beer consumed in the United States have gone up. Thus, there is a positive
Bivariate data consist of ordered _________________.In Exercises 9–12, fill in each blank with the appropriate word or phrase.
In a ________________, ordered pairs are plotted on a set of axes.In Exercises 9–12, fill in each blank with the appropriate word or phrase.
Two variables have a _________________ relationship if the data tend to cluster around a straight line.In Exercises 9–12, fill in each blank with the appropriate word or phrase.
The correlation coefficient measures only the strength of the _________________ relationship between variables.In Exercises 9–12, fill in each blank with the appropriate word or phrase.
Two variables are negatively associated if large values of one variable are associated with large values of the other.In Exercises 13–16, determine whether the statement is true or false. If the
If the correlation coefficient r equals 1, then the points on a scatterplot lie exactly on a straight line.In Exercises 13–16, determine whether the statement is true or false. If the statement is
The correlation coefficient is not resistant.In Exercises 13–16, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
When two variables are correlated, changing the value of one variable will cause a change in value of the other variable.In Exercises 13–16, determine whether the statement is true or false. If the
In Exercises 17–20, compute the correlation coefficient. x 1 y 2 2 34 14 4 3 4 5 7
In Exercises 17–20, compute the correlation coefficient. x 24 13 8 81 63 36 5 y 44 52 42 5 1 48 15
In Exercises 17–20, compute the correlation coefficient. x 5.5 4.2 4.7 5.6 6.0 3.9 6.3 5.7 y 4.9 4.8 4.8 4.7 5.5 5.1 5.8 6.5
In Exercises 17–20, compute the correlation coefficient. x 5 -8 -2 y -1 -3 -6 26 6 9 -10 13 7 -7 -1 5 13 22
In Exercises 21–24, determine whether the correlation coefficient is an appropriate summary for the scatterplot and explain your reasoning.
In Exercises 21–24, determine whether the correlation coefficient is an appropriate summary for the scatterplot and explain your reasoning.
In Exercises 21–24, determine whether the correlation coefficient is an appropriate summary for the scatterplot and explain your reasoning.
In Exercises 21–24, determine whether the correlation coefficient is an appropriate summary for the scatterplot and explain your reasoning.
A person’s age and the person’s income.In Exercises 25–30, determine whether the association between the two variables is positive or negative.
The age of a car and its resale value.In Exercises 25–30, determine whether the association between the two variables is positive or negative.
The age of a car and the number of miles on its odometer.In Exercises 25–30, determine whether the association between the two variables is positive or negative.
The number of times a pencil is sharpened and its length.In Exercises 25–30, determine whether the association between the two variables is positive or negative.
The diameter of an apple and its weight.In Exercises 25–30, determine whether the association between the two variables is positive or negative.
Weekly ice cream sales and weekly average temperature.In Exercises 25–30, determine whether the association between the two variables is positive or negative.
The following table presents the average price in dollars for a dozen eggs and a gallon of milk for each month in a recent year.a. Construct a scatterplot of the price of milk (y) versus the price of
The following table presents the budget (in millions of dollars) for selected organizations that received U.S. government funding for arts and culture in both 2006 and 2016.a. Construct a scatterplot
The following table lists the heights (inches) and weights (pounds) of 14 National Football League quarterbacks in the 2016 season.a. Construct a scatterplot of the weight (y) versus the height
Carbon dioxide (CO2) is produced by burning fossil fuels such as oil and natural gas, and has been connected to global warming. The following table presents the average amounts (in metric tons) of
Foot ulcers are a common problem for people with diabetes. Higher skin temperatures on the foot indicate an increased risk of ulcers. In a study performed at the Colorado School of Mines, skin
The following table presents monthly interest rates, in percent, for 30-year and 15-year fixed-rate mortgages, for a recent year.a. Construct a scatterplot of the 15-year rate (y) versus the 30-year
A blood pressure measurement consists of two numbers: the systolic pressure, which is the maximum pressure taken when the heart is contracting, and the diastolic pressure, which is the minimum
Do larger butterflies live longer? The wingspan (in millimeters) and the lifespan in the adult state (in days) were measured for 22 species of butterfly. Following are the results.a. Construct a
In a survey of cities in the United States, it is discovered that there is a positive correlation between the number of police officers hired by the city and the number of crimes committed. Do you
A survey of U.S. adults showed that there is a negative correlation between age and education level. Does this mean that people become less educated as they become older? Why or why not?
In a sample of adults, would the correlation between age and year graduated from high school be closest to −1, −0.5, 0, 0.5, or 1? Explain.
In a sample of adults, would the correlation between year of birth and year graduated from high school be closest to −1, −0.5, 0, 0.5, or 1? Explain.
A small company has five employees. The following table presents the number of years each has been employed (x) and the hourly wage in dollars (y).a. Compute ̄x, ̄y, sx, and sy.b. Compute the
The following table presents the percentage of students who tested proficient in reading and the percentage who tested proficient in math for each of the 10 most populous states in the United States.
At the final exam in a statistics class, the professor asks each student to indicate how many hours he or she studied for the exam. After grading the exam, the professor computes the least-squares
For each of the following plots, interpret the y-intercept of the least-squares regression line if possible. If not possible, explain why not.a. The least-squares regression line is ŷ = 1.98 +
The Sanchez family wants to sell their house, which is 2800 square feet in size.Mr. Sanchez notices that the slope of the least-squares regression line for predicting price from size is 0.0992. He
When we are given the value of the _____________________ variable, we can use the least-squares regression line to predict the value of the ______________________ variable.In Exercises 5–7, fill in
If the correlation coefficient is equal to 0, the slope of the least-squares regression line will be equal to _____________________ .In Exercises 5–7, fill in each blank with the appropriate word
If the least-squares regression line has slope b1 = 5, and two x-values differ by 3, the predicted difference in the y-values is _____________________.In Exercises 5–7, fill in each blank with the
Substituting the value of the explanatory variable for x in the equation of the least-squares regression line results in a prediction for y.In Exercises 8–12, determine whether the statement is
The least-squares regression line passes through the point of averages (̄x, ̄y).In Exercises 8–12, determine whether the statement is true or false. If the statement is false, rewrite it as a
In general, the slope of the least-squares regression line is equal to the correlation coefficient.In Exercises 8–12, determine whether the statement is true or false. If the statement is false,
The least-squares regression line predicts the result of changing the value of the explanatory variable.In Exercises 8–12, determine whether the statement is true or false. If the statement is
The y-intercept b0 of a least-squares regression line has a useful interpretation only if the x-values are either all positive or all negative.In Exercises 8–12, determine whether the statement is
In Exercises 13–16, compute the least-squares regression line for the given data set. xy 1 2 3 5 5 6 9 7
In Exercises 13–16, compute the least-squares regression line for the given data set. x 95 7 y 3 3 31 13-8-2 6-10 36 0 3 3-2-14
In Exercises 13–16, compute the least-squares regression line for the given data set. x 42 36 14 18 23 36 17 y 72 68 25 31 42 42 65 32
In Exercises 13–16, compute the least-squares regression line for the given data set. x 5.7 5.7 4.1 6.2 4.4 6.5 5.8 4.9 y 1.9 4.8 0.8 3.9 3.9 1.2 1.7 3.0
Compute the least-squares regression line for predicting y from x given the following summary statistics: x = 5 Sy = 100 $x = 2 =2 y = 1350 r = 0.70
Compute the least-squares regression line for predicting y from x given the following summary statistics: x = 8.1 Sy = 1.9 S. Sx = 1.2 y = 30.4 r = -0.85
In a hypothetical study of the relationship between the income of parents (x) and the IQs of their children (y), the following summary statistics were obtained:Find the equation of the least-squares
Assume that in a study of educational level in years (x)and income (y), the following summary statistics were obtained:Find the equation of the least-squares regression line for predicting income
The following table presents the average price in dollars for a dozen eggs and a gallon of milk for each month in a recent year.a. Compute the least-squares regression line for predicting the price

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