Questions and Answers of Statistics Informed Decisions Using Data

What is the linear form of y = abx?
Suppose that data are known to be related through the equation y = axb. What variables need to be transformed to use linear least-squares to estimate a and b?
25 = 32 Change each exponential expression to an equivalent expression involving a logarithm.
x5 = 18 Change each exponential expression to an equivalent expression involving a logarithm.
c3 = 21 Change each exponential expression to an equivalent expression involving a logarithm.
7x = 15 Change each exponential expression to an equivalent expression involving a logarithm.
12x = 43 Change each exponential expression to an equivalent expression involving a logarithm.
53 = y Change each exponential expression to an equivalent expression involving a logarithm.
61.5 = y Change each exponential expression to an equivalent expression involving a logarithm.
log3 81 = 4 Change each logarithmic expression to an equivalent expression involving an exponent.
log4 64 = 3 Change each logarithmic expression to an equivalent expression involving an exponent.
loga 14 = 3 Change each logarithmic expression to an equivalent expression involving an exponent.
logb 19 = 4 Change each logarithmic expression to an equivalent expression involving an exponent.
log4 c = 3 Change each logarithmic expression to an equivalent expression involving an exponent.
log5 b = 4 Change each logarithmic expression to an equivalent expression involving an exponent.
log2 5 = k Change each logarithmic expression to an equivalent expression involving an exponent.
log6 24 = w Change each logarithmic expression to an equivalent expression involving an exponent.
log3(uv)Write each expression as a sum of logs. Express powers as factors.
log2(ab)Write each expression as a sum of logs. Express powers as factors.
log5 x4 Write each expression as a sum of logs. Express powers as factors.
log7 y3 Write each expression as a sum of logs. Express powers as factors.
loga(uv2)Write each expression as a sum of logs. Express powers as factors.
loga(x3y)Write each expression as a sum of logs. Express powers as factors.
log(x4y3)Write each expression as a sum of logs. Express powers as factors.
log(x6y2)Write each expression as a sum of logs. Express powers as factors.
log 34Use a calculator to evaluate each expression. Round your answers to three decimal places.
log 18 Use a calculator to evaluate each expression. Round your answers to three decimal places.
log 13.2 Use a calculator to evaluate each expression. Round your answers to three decimal places.
log 34.1 Use a calculator to evaluate each expression. Round your answers to three decimal places.
101.6 Use a calculator to evaluate each expression. Round your answers to three decimal places.
102.3 Use a calculator to evaluate each expression. Round your answers to three decimal places.
100.36 Use a calculator to evaluate each expression. Round your answers to three decimal places.
100.74 Use a calculator to evaluate each expression. Round your answers to three decimal places.
The following data, obtained from the U.S. Census Bureau, represent the population of the United States. An ecologist is interested in finding an equation that describes the population of the United
The following data represent the amount of money an investor has in an investment account each year for the last 6 years. The theory of finance states that account values grow exponentially over
David is conducting an experiment to estimate the acceleration of an object due to gravity. He takes a ball, drops it from different heights, and records the time that it takes for the ball to hit
Cathy is conducting an experiment to measure the relation between a light bulb’s intensity and the distance from the light source. She measures a 100-watt light bulb’s intensity 1 meter from the
The period of a pendulum is the time required for one oscillation; the pendulum is usually referred to as simple when the angle made with the vertical is less than 5°. An experiment is conducted in
Depreciation The following data represent the asking price, y, and age, x, of a Chevrolet Impala(a) Determine the linear least-squares regression line, treating age as the explanatory variable. Plot
Go to the book’s website and download the file 4_5_46. The data represent the percentage of putts made by golfers on the PGA Tour at different distances from the hole. For example, at a distance of
The data shown in Table 17 show the finishing times (in minutes) of the men in the 60- to 64- year-old age group in a 5-kilometer race. Determine the five-number summary of the data.Approach The
Using statistical software or a graphing calculator, determine the five-number summary of the data presented in Table 17.Approach We will use Minitab to obtain the five-number summary. Table 17 19.95
Use the results from Example 1 to construct a boxplot of the finishing times of the men in the 60- to 64-year-old age group.Data from Example 1The data shown in Table 17 show the finishing times (in
In the Spacelab Life Sciences 2, led by Paul X. Callahan, 14 male rats were sent to space. The red blood cell mass (in milliliters) of the rats was determined when they returned. A control group of
A golf pro wants to investigate the relation between the club-head speed of a golf club (measured in miles per hour) and the distance (in yards) that the ball will travel. He realizes other variables
For the data shown in Table 2, compute the linear correlation coefficient. A scatter diagram of the data is shown in Figure 6. The dashed lines on the scatter diagram represent the mean of x and the
Use a statistical spreadsheet or a graphing calculator with advanced statistical features to draw a scatter diagram of the data in Table 1. Then determine the linear correlation between club-head
Using the results from Example 3, determine whether a linear relation exists between club-head speed and distance.Data from Example 3Use a statistical spreadsheet or a graphing calculator with
Because colas tend to replace healthier beverages and colas contain caffeine and phosphoric acid, researchers Katherine L. Tucker and associates wanted to know whether cola consumption is associated
The data in Table 5 represent the club-head speed and the distance a golf ball travels for eight swings of the club. We found that these data are linearly related .(a) Find a linear equation that
Find the least-squares regression line for the data in Table 2 from Section 4.1.Approach We foundSubstitute the values in Formulas (2) and (3) to find the slope and intercept of the least-squares
Use the golf data in Table 5.(a) Find the least-squares regression line.(b) Draw the least-squares regression line on the scatter diagram of the data.(c) Predict the distance a golf ball will travel
Compare the sum of squared residuals for the lines in Examples 1 and 3.Approach Use a table to compute ∑residuals2 using the predicted values of y, ŷ, for the equations in Examples 1 and 3.Data
Determine and interpret the coefficient of determination, R2, for the clubhead speed versus distance data shown in Table 5 on page 225.By Hand ApproachTo compute R2, we square the linear correlation
The data in Table 8 were collected by placing a temperature probe in a portable heater, removing the probe, and recording the temperature (in degrees Fahrenheit) over time (in seconds). Determine
Figure 23(a) shows a scatter diagram of a set of data. The residual plot is shown in Figure 23(b) and the boxplot of the residuals is in Figure 23(c). Do the data have any outliers?Approach We
The data in Table 6 on page 232 represent the club-head speed, the distance the golf ball traveled, and the residuals (Column 7) for eight swings of a golf club. Construct a residual plot and boxplot
Suppose that our golf ball experiment calls for nine trials, but the player that we are using hurts his wrist. Luckily, Bubba Watson is practicing on the same range and graciously agrees to
Find the frequency marginal distributions for employment status and level of education from the data in Table 9.Approach Find the row total for the category “employed” by adding the number of
Determine the relative frequency marginal distribution for level of education and employment status from the data in Table 10.Approach The relative frequency marginal distribution for the row
What proportion of the following groups of individuals is employed?(a) Those who did not finish high school (b) High school graduates(c) Those who finished some college (d) Those who have at least a
Find the conditional distribution of the response variable employment status by level of education, the explanatory variable, for the data in Table 9 on page 253.What is the association between level
Using the results of Example 4, draw a bar graph that represents the conditional distribution of employment status by level of education.Approach When drawing conditional bar graphs, label the values
The data in Table 13 show the admission status and gender of students who applied to the University of California, Berkeley. From the data in Table 13, the proportion of accepted applications is
The data in Table 1 represent the first exam score of 10 students enrolled in Introductory Statistics. Treat the 10 students as a population.(a) Compute the population mean.(b) Find a simple random
The data in Table 2 represent the length (in seconds) of a random sample of songs released in the 1970s. Find the median length of the songs.Approach Follow the steps listed above. Table 2 Song Name
Find the median score of the data in Table 1.Approach Follow the steps listed on the previous page. Table 1 Student Score 1. Michelle 82 2. Ryanne 77 3. Bilal 90 4. Pam 71 5. Jennifer 62 6. Dave 68
Yolanda wants to know how much time she typically spends on her cell phone. She goes to her phone’s website and records the call length for a random sample of 12 calls, shown in Table 3. Find the
The data in Table 5 represent the birth weights (in pounds) of 50 randomly sampled babies.(a) Find the mean and the median birth weight.(b) Describe the shape of the distribution.(c) Which measure of
The following data represent the number of O-ring failures on the shuttle Columbia for its 17 flights prior to its fatal flight:0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 3 Find the mode number
Find the mode of the exam score data listed in Table 1, which is repeated here:82, 77, 90, 71, 62, 68, 74, 84, 94, 88Approach Tally the number of times we observe each data value. The data value
The data in Table 6 represent the location of injuries that required rehabilitation by a physical therapist. Determine the mode location of injury.Approach Determine the location of injury that
Sample: 25, 14, 1, 5, 10 Find the population mean or sample mean as indicated.
Population: 2, 5, 15, 16, 12 Find the population mean or sample mean as indicated.
For a large sporting event, broadcasters sold 66 ad slots for a total revenue of $164 million. What was the mean price per ad slot?
The median for the given set of six ordered data values is 30.5.What is the missing value? 5 12 25 41 58
An insurance company crashed four cars of the same model at 5 miles per hour. The cost of repair for each of the four crashes was $$434$, $$413$, $$452$, and $$241$. Compute the mean, median,
The following data represent the amount of time (in minutes) a random sample of eight students took to complete the online portion of an exam in a particular statistics course.Compute the mean,
A concrete mix is designed to withstand 3000 pounds per square inch (psi) of pressure. The following data represent the strength of nine randomly selected casts (in psi). 3950, 4080, 3300, 3100,
The acidity or alkalinity of a solution is measured using pH. A pH less than 7 is acidic; a pH greater than 7 is alkaline. The accompanying data represent the pH in samples of bottled water and tap
A sample of 20 registered voters was surveyed in which the respondents were asked, “Do you think Chang, Johnson, Ohm, or Smith is most qualified to be a senator?” The results of the survey are
Mr. Zuro finds the mean height of all 15 students in his statistics class to be 67.0 inches. Just as Mr. Zuro finishes explaining how to get the mean, Danielle walks in late. Danielle is 63.8 inches
Missing Exam Grade A professor has recorded exam grades for 20 students in his class, but one of the grades is no longer readable. If the mean score on the exam was 80 and the mean of the 19 readable
In January 2015, the mean amount of money lost per visitor to a local riverboat casino was $135. Do you think the median was more than, less than, or equal to this amount? Why?
The data in Table 7 represent the IQ scores of a random sample of 100 students from two different universities. For each university, compute the mean IQ score and draw a histogram using a lower class
The data in Table 8 represent the scores on the first exam of 10 students enrolled in Introductory Statistics. Compute the range.Approach The range is the difference between the largest and smallest
Compute the population standard deviation of the test scores in Table 8.Approach Using Formula (1)Step 1 Create a table with four columns. Enter the population data in Column 1. In Column 2, enter
Compute the sample standard deviation of the sample obtained in Example 1 (b) from Section 3.1.Approach We follow the same approach that we used to compute the population standard deviation, but this
Use statistical software or a calculator to determine the population standard deviation of the data listed in Table 8 and the sample standard deviation of the sample data from Example 4.Approach We
Refer to the data in Example 1. Use the standard deviation to determine whether University A or University B has more dispersion in its students’ IQ scores.Approach We will use Minitab to determine
Use the results of Examples 3 and 4 to determine the population and sample variance of test scores on the statistics exam.Approach The population variance is found by squaring the population standard
Use the data from University A in Table 7.(a) Determine the percentage of students who have IQ scores within 3 standard deviations of the mean according to the Empirical Rule.(b) Determine the
Use the data from University A in Table 7.(a) Determine the minimum percentage of students who have IQ scores within 3 standard deviations of the mean according to Chebyshev’s Inequality.(b)
Sample: 23, 12, 6, 8, 9 By hand, find the population variance and standard deviation or the sample variance and standard deviation as indicated.
Sample: 4, 13, 25, 31, 37 By hand, find the population variance and standard deviation or the sample variance and standard deviation as indicated.
Sample: 4, 46, 14, 51, 32, 23, 28, 30, 36, 27 By hand, find the population variance and standard deviation or the sample variance and standard deviation as indicated.
An insurance company crashed four cars in succession at 5 miles per hour. The cost of repair for each of the four crashes was $$422$, $$454$, $$419$, $$215$. Compute the range, sample
Compute the range and sample standard deviation for the strength of this concrete (in psi).3930, 4080, 3500, 3000, 2950, 3870, 4080, 4040
The following data represent the flight time (in minutes) of a random sample of seven flights from one city to another city.284, 270, 260, 266, 257, 263, 269 Compute the range and sample standard
The accompanying data represent the pulse rates (beats per minute) of nine students enrolled in a statistics course. Treat the nine students as a population.(a) Compute the population standard

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