Math 101 3A, 3C, 3D, 5C, 5D
The wholesale price of a TV is 55% less than retail price. Therefore, the wholesale price is _____ times the retail price.
0.45 100-55=45 45/100
The gestation period of horses (336 days) is _____ percent longer than the gestation period of lions (108 days).
211.1 108-336= then /108
Simon's monthly take-home pay (after taxes) is $2100. If he pays 19 % of his gross pay (before taxes) in tax, what is his gross pay?
2593 (100-19)= 81 2100/.81= 2593
The true price of a gift you purchase by mail-order is $18.98, but you are billed for $ 19.86. Find the absolute and relative errors.
Absolute: 0.88 Relative: 4.6 0.88/18.98
How can the graphics sometimes be useful? A. It can make it easier to show data that spans a very large range. B. It can make it easier to show small scale trends in the data. Your answer is correct.C. It can make it easier to show large scale trends in the data.
B
An 18th-century philosopher once said, "A penny saved is a penny earned," but if he were alive today, he would be talking about a dollar rather than a penny. Choose the correct answer below. A. The statement does not make sense. The value of a penny is always 1 cent. B. The statement makes sense. Due to inflation, a penny in the 18th century has less purchasing power than a penny today. C. The statement makes sense. Due to inflation, a penny in the 18th century has about the same purchasing power as a dollar today. Your answer is correct.D. The statement does not make sense. Due to inflation, a penny in the 18th century has less purchasing power than a penny today.
C
Determine whether the data described are qualitative or quantitative. The heights of subjects in a clinical trial of a new drug Choose the correct answer below.
quantitative
Determine whether the data described are qualitative or quantitative. The shoe sizes left parenthesis such as 8 or 10 and one half right parenthesis of test subjects Choose the correct answer below.
quantitative
State whether the following statement is true or false, and explain why. If the statement is false, state the true change. If the profits in your consulting business increase by 5% one year and decrease by 3% the following year, your profits are up by 2% over two years.
False; If the profits in your consulting business increase by 5% one year and decrease by 3% the following year, your profits are up by 1.85% over two years.
Express the given fraction as a decimal and a percentage. nine eighths What is the decimal form of nine eighths ?
1.125 112.5%
Give an example in which the absolute error is small but the relative error is large. A. A chemist has 2.9 mg of substance, but a scale measures 2.1 mg. Your answer is correct.B. A runner's true weight is 125 pounds, but a scale says he weighs 130 pounds. C. A census says that the population of a town is 72,453, but the true population is 96,000. D. A woman weighs 102.4 pounds. The scale at the gym says she weighs 102.7, but the scale at the doctor's office says she weighs 102one fourth .
A
Compare the following pair of numbers A and B in three ways. a. Find the ratio of A to B. b. Find the ratio of B to A. c. Complete the sentence: A is ____ percent of B. A equals 130 and B equals 360
A. 13/36 B. 36/13 C. 36.1
Despite the fact that the new drug lowered blood pressure more than the old drug did in both the men and the women in the study, an overall analysis shows that the old drug was actually more effective. Choose the correct answer below. A. The statement does not make sense because it is impossible for the cure rate to be higher for men and women and not higher over all. B. The statement does not make sense because there is no information given about the sampling method or about how the trials of the test were divided. C. The statement makes sense because there is no information given about the sampling method or about how the trials of the test were divided. Your answer is correct.D. The statement makes sense because because it is impossible for the cure rate to be higher for men and women and not higher over all.
C
What is meant by cumulative frequency? A. The cumulative frequency of a category is the number of data values in that category and all later categories. B. The cumulative frequency of a category is the number of data values in that category. C. The cumulative frequency of a category is the number of data values in that category and all preceding categories. Your answer is correct.D. Cumulative frequencies are groups of data that cover a range of possible values.
C
Carry out the indicated operation and give your answer with 2 significant digits. 245.78 divided by 0.028 What is 245.78 divided by 0.028 with two significant digits?
8,800
When we chart the price of milk in 1995 dollars we find that it has become slightly more expensive, but when we chart it in 1975 dollars we find that it has become cheaper. Choose the correct answer below. A. The statement does not make sense because the same trend would be seen regardless of what kind of dollars are used. Your answer is correct.B. The statement makes sense because 1995 dollars are worth more than 1975 dollars. C. The statement does not make sense because prices always rise with time. D. The statement makes sense because 1975 dollars are worth more than 1995 dollars.
A
What are significant digits? A. Significant digits are the digits that occur in a result because of random and inherently unpredictable events in the measurement process. B. Significant digits are the digits in a number that represent actual measurements and therefore have meaning. Your answer is correct.C. Significant digits are the digits that describe how closely the measurement approximates the true value.
B
How can the graphics sometimes be misleading? A. The actual data values cannot be found on the graph. B. The values do not line up with the axes in the normal way. C. The variation can seem to be larger than it really is. Your answer is correct.D. The variation can seem to be smaller than it really is.
C
The sales tax rate in a city is 8.7%. Find the tax charged on a purchase of $268, and the total cost.
How much tax is charged on a purchase of $268? 23.32 Sales Taxequals Sales Tax Rate times Purchase Price Tequals8.7% times $268 Tequals48.7 times 0.01 times $268 Tequals0.087 times $268 Tequals$23.32 What is the total price? 291.32 23.32+268
Explain what is meant by the categories and frequencies. Choose the correct answer below. A. Categories are descriptions of data, such as which grades students received on a test or the heights of trees in a forest. They can describe qualities or represent counts or measurements. The frequency of a category is the number of data values in the category. Your answer is correct.B. Categories are descriptions of data, such as which brand names of shoes sold in a store or audience ratings of films. They always describe qualities. The frequency of a category is the number of data values in the category. C. Frequencies are descriptions of data, such as which grades students received on a test or the heights of trees in a forest. They can describe qualities or represent counts or measurements. The category of a frequency is the number of data values in the frequency. D. Categories are descriptions of data, such as ages of people living in a city or the annual salaries of professional athletes. They always represent counts or measurements. The frequency of a category is the number of data values in the category.
A
Find the absolute and relative errors in the following situation. Your true height is 69.0 inches (5 ' 9 ''), but a nurse in your doctor's office measures your height as 69.3 inches.
Absolute: 0.3 Relative: 0.4 69.3-69=0.3 0.3/69
How are their meanings related? A. If the compared value is P% of the reference value, it is (100minusP)% more than the reference value. B. If the compared value is P% more than the reference value, it is (100plusP)% of the reference value. Your answer is correct.C. If the compared value is P% more than the reference value, it is (100minusP)% of the reference value. D. If the compared value is P% of the reference value, it is (100plusP)% more than the reference value.
B
How would you verify the detection rates? A. Divide the total number of false negatives by the total number of patients. B. Divide the total number of true negatives by the total number of patients. C. Divide the total number of false positives by the total number of patients. D. Divide the total number of true positives by the total number of patients.
D
Express the given percentage as a reduced fraction and a decimal. 220% What is the reduced fraction form of 220%?
11/5
In the following statement, express the first number as a percentage of the second number. The full-time year-round median salary for U.S. men in 2010 was $41 comma 800, and the full-time year-round salary for U.S. women in 2010 was $34 comma 300.
121.9%
Fill in the blank. Will is 23% taller than Wanda, so Will's height is ____% of Wanda's height.
123%
Carry out the indicated operation and give your answer with the specified number of significant digits. 43 times 32.1; 3 significant digits
1380
Use the appropriate rounding rules to do the following calculations. Express the result with the correct precision or correct number of significant digits. What is the per capita cost of a $2.2 million recreation center in a city with 140 ,461 people?
16
Use the appropriate rounding rules to do the following calculations. Express the result with the correct precision or correct number of significant digits. Divide 104 miles by 0.65 hours.
160
State the number of significant digits and the implied precision of the given number. 1.296 times 10 Superscript 4 seconds
4
State the number of significant digits and the implied precision of the given number. 2772 dollars per acre
4
Express the first number as a percentage of the second number. 24 pounds of recyclable trash in a barrel of 54 pounds of trash
44.4%
A company decided to expand, so it opened a factory, generating 455 jobs. For the 70 white-collor positions, 200 males and 200 females applied. Of the females who applied, 20% were hired, while only 15% of the males were hired. Of the 400 males applying for the blue-collar positions, 75% were hired, while 85% of the 100 females who applied were hired. Answer the questions below. How does looking at the white-collar and blue-collar positions separately suggest a hiring preference for women? A. The number of women hired is greater than the number of men hired when the two types of positions are condsidered separately. Your answer is not correct.B. The number of women hired for white-collar positions is higher than the number of men hired for blue-collar positions when the two types of positions are considered separately. C. The percentages of women hired are higher than the percentages of men hired when the two types of positions are considered separately.
A
Distinguish between the absolute error and the relative error in a measurement. Give an example in which the absolute error is large but the relative error is small and another example in which the absolute error is small but the relative error is large. Distinguish between the absolute error and the relative error in a measurement. A. The absolute error describes how far a measured (or claimed) value lies from the true value. The relative error compares the size of the absolute error to the true value and is often expressed as a percentage. Your answer is correct.B. The absolute error describes how far a measured (or claimed) value lies from the relative error. The relative error compares the size of the absolute error to the relative error and is often expressed as a percentage. C. The relative error describes how far a measured (or claimed) value lies from the absolute error. The absolute error compares the size of the relative error to the true value and is often expressed as a percentage. D. The relative error describes how far a measured (or claimed) value lies from the true value. The absolute error compares the size of the relative error to the true value and is never expressed as a percentage.
A
How can you tell whether zeros are significant? A. The position of zeros in a number with respect to the position of the nonzero numbers in a number is what determines the significance of zeros. Your answer is correct.B. Trailing and leading zeros are never significant, where as zeros contained between nonzero digits are always significant. C. Zeros are never significant. D. Zeros are always significant.
A
There's been only a very slight rise in our stock price over the past few months, but I wanted to make it look dramatic so I started the vertical scale from the lowest price rather than from zero. Choose the correct answer below. A. The statement makes sense because reducing the range of the vertical axis to just fit the data will increase the relative size of the variation in the data. Your answer is correct.B. The statement makes sense because increasing the range of the vertical axis to contain all of the data will increase the relative size of the variation in the data. C. The statement does not make sense because reducing the range of the vertical axis to just fit the data will decrease the relative size of the variation in the data. D. The statement does not make sense because changing the axis cannot change the data that is being displayed.
A
What is meant by relative frequency? A. The relative frequency of a category is the fraction (or percentage) of the data values that fall in that category. Your answer is correct.B. The relative frequency of a category is the number of data values in that category. C. Relative frequencies are groups of data that cover a range of possible values. D. The relative frequency of a category is the number of data values in that category and all preceding categories.
A
What is the distinction between qualitative data and quantitative data? Give a few examples of each. Choose the correct answer below. A. Qualitative data describe categories, while quantitative data represent counts or measures. Brand names of shoes in a consumer survey and eye colors are examples of qualitative data. Heights of students and quiz scores are examples of quantitative data. Your answer is correct.B. Quantitative data describe categories, while qualitative data represent counts or measures. Brand names of shoes in a consumer survey and eye colors are examples of qualitative data. Heights of students and quiz scores are examples of quantitative data. C. Qualitative data describe categories, while quantitative data represent counts or measures. Brand names of shoes in a consumer survey and eye colors are examples of quantitative data. Heights of students and quiz scores are examples of qualitative data. D. Quantitative data describe categories, while qualitative data represent counts or measures. Brand names of shoes in a consumer survey and eye colors are examples of quantitative data. Heights of students and quiz scores are examples of qualitative data.
A
What is the third way to use percentages? A. Percentages can be used to compare two things. For example, the car costs 25% more but gets 10% more miles per gallon. Your answer is correct.B. Percentages can be used to express a fraction of something. For example, this class scored 10% better, but took 50% longer. C. Percentages can be used to express a fraction of something. For example, the average test score dropped 5% from last year. D. Percentages can be used to compare two things. For example, out of 250 cars, 30% are green.
A
Why can it be misleading to give measurements with more precision than is justified by the measurement process? Choose the correct answer below. A. It is misleading because the measurement would be perceived as having a greater amount of detail than it actually has. Your answer is correct.B. It is misleading because the measurement would be perceived as having a lesser amount of detail than it actually has. C. It is misleading because the measurement would be perceived to be closer to the true value than it actually is. D. It is misleading because the measurement would be perceived to be further from the true value than it actually is.
A
Find the absolute change and the percentage change in the following case. The number of daily news paper in a country was 2149 in 1900 and 1313 in 2010.
Absolute Change: -836 1313-2149= -836 Percentage Change: -39 -836/2149 x100
Find the absolute and relative errors in the following situation. The diameter of a gear must be 24.4 centimeters in order for it to fit in a transmission. Instead, it is manufactured with a diameter of 24.28 centimeters.
Absolute: -0.12 Relative: -0.5
Baggage screening machines are 98% accurate in identifying bags that contain banned materials. Therefore, if the screening shows a bag that contains banned materials, then it almost certainly does. Choose the correct answer below. A. The statement makes sense because, depending on the proportion of true positives to total positives, the actual percentage of bags that show banned materials and actually have banned materials could be quite high. B. The statement does not make sense because, depending on the proportion of true positives to total positives, the actual percentage of bags that show banned materials and actually have banned materials could be quite low. Your answer is correct.C. The statement makes sense because, depending on the proportion of true positives to total positives, the actual percentage of bags that show banned materials and actually have banned materials could be quite low. D. The statement does not make sense because, depending on the proportion of true positives to total positives, the actual percentage of bags that show banned materials and actually have banned materials could be quite high.
B
By turning off her lights and closing her windows at night, Maria saved 118% on her monthly energy bill. Choose the correct answer below. A. The claim could be true because her new monthly energy bill would be 82% of the previous monthly energy bill, which makes sense. B. The claim could not be true because her new monthly energy bill would be minus18% of the previous monthly energy bill. This is impossible since the bill cannot be negative. Your answer is correct.C. The claim could not be true because her new monthly energy bill would be minus82% of the previous monthly energy bill. This is impossible since the bill cannot be negative. D. The claim could be true because her new monthly energy bill would be 18% of the previous monthly energy bill, which makes sense.
B
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. If John earns 20% more than Mary does, then Mary must earn 20% less than John does. Choose the correct answer below. A. The statement makes sense because 20% is the absolute difference between John and Mary. B. The statement does not make sense because if John earns 20% more than Mary, then Mary must earn approximately 16.7% less than John does. Your answer is correct.C. The statement does not make sense because if John earns 20% more than Mary, then Mary must earn 80% less than John does. D. The statement makes sense because the relative difference is 20% and it does not change by switching the reference value and the compared value.
B
Describe possible sources of random and systematic errors in the following measurement. The weights reported to the pilot of a small plane when the pilot asks what the passengers weigh. Choose the correct answer below. A. Random errors could not occur, but systematic errors could occur when people intentionally lie about their weight by reporting a value that is considerably lower than the true weight. B. Random errors could occur when people do not know their actual weight and report an amount that is wrong. Systematic errors could occur when people intentionally lie about their weight by reporting a value that is considerably lower than the true weight. Your answer is correct.C. Random errors could occur when people forget that they lost weight recently and report an amount that is too high. Systematic errors could occur when people intentionally lie about their weight by reporting a value that is considerably higher than the true weight.
B
Explain the difference between graphics that only appear three-dimensional and those that show truly three-dimensional data. Choose the correct answer below. A. Truly three-dimensional graphics use actual three-dimensional objects to represent data. Graphics that only appear three-dimensional show images of three-dimensional obects being used to represent data. B. Truly three-dimensional graphics show data with 3 different variables plotted along three different axes. Graphics that only appear three-dimensional show data with less than three different axes, but parts of the graphic look three-dimensional. Your answer is correct.C. Truly three-dimensional graphics allow the viewer to change the viewpoint interactively. Graphics that only appear three-dimensional show a three-dimensional data set from a single static viewpoint.
B
Suppose a positive result is that the test results show not lying/no drug use. Also, assume the probability of lying/drug use is very low. Choose the correct answer below. A. Since the probabilities of both a false negative and a true negative are very high, the proportion of false negatives to total negatives will be low. B. Since the probabilities of both a false negative and a true negative are very low, the proportion of false negatives to total negatives will be large. Your answer is correct.C. Since the probabilities of both a false positive and a true positive are very low, the proportion of false positives to total positives will be large.
B
The Department of Health of a certain state estimates a 10% rate of HIV for the "at risk" population and a 0.3% rate for the general population. Tests for HIV are 95% accurate in detecting both true negatives and true positives. Random selection of 5000 "at risk" people and 20,000 people from the general population results in the following table. Use the table below to complete parts (a) through (e)a. Verify that incidence rates for the general and "at risk" populations are 0.3% and 10%, respectively. Also, verify that detection rates for the general and "at risk" populations are 95%. How would you verify the incidence rates? A. Divide the number of uninfected patients by the total number of patients. B. Divide the number of infected patients by the total number of patients. Your answer is correct.C. Divide the number of infected patients by the number of uninfected patients. D. Divide the number of uninfected patients by the number of infected patients.
B
The price per gallon of gasoline has risen from only a quarter in 1918 to nearly $3 in 2009, thereby making it much more difficult for the poor to afford fuel for their cars. Choose the correct answer below. A. The statement does not make sense because "poor" is too vague a description to be meaningful in this context. B. The statement does not make sense because when inflation is taken into account, the two prices are quite comparable. Your answer is correct.C. The statement makes sense because even with inflation taken into account, the price per gallon of gasoline in 1918 was much less than the price in 2009. D. The statement makes sense. Gasoline is twelve times as expensive today compared to 1918, so it makes sense that it is more difficult for the poor to afford fuel for their cars.
B
The rate of return on our fund increased by 50%, to 15%. Choose the correct answer below. A. The statement does not make sense because if the rate of return on our fund increased by 50%, to 15%, then the previous rate is minus35%, which does not make sense. B. The statement makes sense because if the rate of return on our fund increased by 50%, to 15%, then the previous rate is 10%, which makes sense. Your answer is correct.C. The statement makes sense because if the rate of return on our fund increased by 50%, to 15%, then the previous rate is 7.5%, which makes sense. D. The statement does not make sense because if the rate of return on our fund increased by 50%, to 15%, then the previous rate is 65%, which does not make sense.
B
What are three-dimensional graphics? A. Three-dimensional graphics are physical objects that are created for representing complex data sets. B. Three-dimensional graphics are graphs that visualize data using images that look three dimensional. Your answer is correct.C. Three-dimensional graphics are graphs that show the same information for three or more different data sets. D. Three-dimensional graphics are graphics that are interactive.
B
What is the Consumer Price Index (CPI)? How is it supposed to be related to inflation? Choose the correct answer below. A. It is a way of comparing the prices consumers pay for products to the prices producers (manufacturers) pay for the goods they purchase. It allows one to see how prices have changed with time, and therefore measures inflation. B. It is a way of measuring the prices consumers pay for products. It allows one to see how prices have changed with time, and therefore measures inflation. C. It is a way of measuring consumer attitudes. It can gauge whether people are likely to be spending or saving, which, in turn, is related to inflation.
B
What two types of graphs are most common when the categories are qualitative data? Describe the construction of each. Select the two choices below that correctly answer the question above. A. In a bar graph, each category corresponds to a wedge of a circle. The size of each wedge is proportional to the relative frequency of the category it represents. B. In a pie chart, each category corresponds to a wedge of a circle. The size of each wedge is proportional to the relative frequency of the category it represents. Your answer is correct.C. In a frequency table, each category corresponds to a wedge of a circle. The size of each wedge is proportional to the relative frequency of the category it represents. D. A frequency table has two columns. The first column lists all of the categories of data. The second column lists the frequency of each category. E. In a pie chart, the categories are clearly indicated along the horizontal axis. Over each category is a rectangle whose height indicates the frequency or relative frequency of the category. Numbers along the vertical axis clearly indicate the scale. F. In a bar graph, the categories are clearly indicated along the horizontal axis. Over each category is a rectangle whose height indicates the frequency or relative frequency of the category. Numbers along the vertical axis clearly indicate the scale.
B and F
A company decided to expand, so it opened a factory, generating 455 jobs. For the 70 white-collor positions, 200 males and 200 females applied. Of the females who applied, 20% were hired, while only 15% of the males were hired. Of the 400 males applying for the blue-collar positions, 75% were hired, while 85% of the 100 females who applied were hired. Answer the questions below. How does looking at the white-collar and blue-collar positions separately suggest a hiring preference for women? A. The number of women hired is greater than the number of men hired when the two types of positions are condsidered separately. Your answer is not correct.B. The number of women hired for white-collar positions is higher than the number of men hired for blue-collar positions when the two types of positions are considered separately. C. The percentages of women hired are higher than the percentages of men hired when the two types of positions are considered separately.
C
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. My older child weighs 25% more than my younger child. Choose the correct answer below. A. The statement makes sense because if the older child weighs 25% more than the younger child, then his weight is 0.75 times the younger child's weight, which is possible. B. The statement does not make sense because if the older child weighs 25% more than the younger child, then his weight is minus1.25 times the younger child's weight. This cannot be true because the weight is never negative. C. The statement makes sense because if the older child weighs 25% more than the younger child, then his weight is 1.25 times the younger child's weight, which is possible. Your answer is correct.D. The statement does not make sense because if the older child weighs 25% more than the younger child, then his weight is minus0.75 times the younger child's weight. This cannot be true because the weight is never negative.
C
Determine whether the data described below are qualitative or quantitative and explain why. The structural statuses of bridges left parenthesis sound or unsound right parenthesis in a study of infrastructure Choose the correct answer below. A. The data are quantitative because they don't measure or count anything. B. The data are quantitative because they consist of counts or measurements. C. The data are qualitative because they don't measure or count anything. Your answer is correct.D. The data are qualitative because they consist of counts or measurements.
C
Explain the difference between the key words 'of' and 'more than' when dealing with percentages. How are their meanings related? Explain the difference. Choose the correct answer below. A. The key word 'more than' is used to express the ratio of the compared value to the relative value. The key word 'of' is used to express the relative change between the referenced value and the compared value. B. The key word 'more than' is used to express the ratio of the compared value to the relative value. The key word 'of' is used to express the absolute change between the referenced value and the compared value. C. The key word 'more than' is used to express the relative change between the referenced value and the compared value. The key word 'of' is used to express the ratio of the compared value to the referenced value. Your answer is correct.D. The key word 'more than' is used to express the absolute change between the referenced value and the compared value. The key word 'of' is used to express the ratio of the compared value to the referenced value.
C
Two candidates for governor of a state differ in their accounts of the state's economy during the incumbent's term. The incumbent claims that during his four-year term the economy has improved, citing a rise in the median household income from $ 33 comma 000 to $ 34 comma 500. The challenger claims that the economy has declined, citing that the buying power of families in the state has declined during the four years. Which of the following best explains how both candidates can be right? A. It is not possible for both candidates to be right; one of them is obviously lying. B. Only those in the middle income group saw their incomes rise, those with lower and higher incomes actually saw their incomes decline during the incumbent's term. C. Though the median household income increased, prices increased by a greater percent, meaning that in real terms the median income actually decreased. Your answer is correct.D. The incumbent is referring to the state economy, while the challenger is referring to the national economy.
C
We found that these rare cancers were 700% more common in children living near the toxic landfill than in the general population. Choose the correct answer below. A. The statement does not make sense because the number of rare cancers found in the general population is 7 times the number of rare cancers found in children living near the toxic landfill, which does not make sense. B. The statement makes sense because the number of rare cancers found in children living near the toxic landfill is 7 times the number of rare cancers found in the general population, which is possible. C. The statement makes sense because the number of rare cancers found in children living near the toxic landfill is 8 times the number of rare cancers found in the general population, which is possible. Your answer is correct.D. The statement does not make sense because the number of rare cancers found in the general population is 8 times the number of rare cancers found in children living near the toxic landfill, which does not make sense.
C
Wilma used a yard stick to measure the length of her kitchen to the nearest micrometer. Choose the correct answer below. A. The statement makes sense because yards are the English system equivalent to micrometers. Therefore, the measurement will be precise to the nearest micrometer. B. The statement makes sense because yards and micrometers are both units of length and it is easy to convert between the two without consequence. Therefore, the measurement will be precise to the nearest micrometer. C. The statement does not make sense because a yard stick measures length in yards not micrometers. Therefore, the measurement will not be precise to the nearest micrometer.
C
c. Discuss interesting features of the data revealed by the display. Choose the correct answer below. A. Religion D has by far the largest percentage value and religion C has the second largest percentage value. The percentage values for the other religions are relatively similar in magnitude. B. There appears to be no percentage that is significantly larger or smaller than the rest of the percentage values. All the data values are roughly the same size. C. Religion C has by far the largest percentage value and religion D has the second largest percentage value. The percentage values for the other religions are relatively similar in magnitude. Your answer is correct.D. The percentage increases steadily from religion B to religion E and remains constant from E to F. Religion E has the largest percentage value in the sample.
C
A $1 million error may sound like a lot, but when compared to our company's revenue it represents a relative error of only 0.1%. Choose the correct answer below. A. The statement does not make sense because the relative error is low. Thus, the $1 million dollar error is not very big when compared with the actual revenue. B. The statement makes sense because the relative error is high. Thus, the $1 million dollar error is very big when compared with the actual revenue. C. The statement does not make sense because the relative error is high. Thus, the $1 million dollar error is very big when compared with the actual revenue. D. The statement makes sense because the relative error is low. Thus, the $1 million dollar error is not very big when compared with the actual revenue.
D
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. I was unable to make a bar chart, because the data categories were qualitative rather than quantitative. Choose the correct answer below. A. The statement does not make sense because histograms are commonly used to show data when the categories are qualitative. B. The statement makes sense because bar graphs are commonly used to show data when the categories are qualitative. C. The statement makes sense because bar graphs are commonly used to show data when the categories are quantitative. D. The statement does not make sense because bar graphs are commonly used to show data when the categories are qualitative.
D
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. My bar chart contains more information than yours, because I made my bars three-dimensional. Choose the correct answer below. A. The statement makes sense because making the bars three-dimensional makes the graph easier to read and increases the amount of information that can be read from it. B. The statement makes sense because making the bars three-dimensional means that more information was used to create a third dimension in the graph. C. The statement does not make sense because making the bars three-dimensional makes the graph harder to read and reduced the amount of information that can be read from it. D. The statement does not make sense because making the bars three-dimenional does not necessarily mean that information was added. It could mean that only the appearance of the graph was changed.
D
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. Your bar graph must be wrong, because your bars are wider than the ones shown on the teacher's answer key. Choose the correct answer below. A. The statement makes sense because if your bars are wider than the teacher's, then your bars must also be shorter than the teacher's, therefore your graph is wrong. B. The statement makes sense because the width of the bars in a bar graph does affect the accuracy of the graph. The width of the bars on your graph must represent the same category or interval as the teacher's graph and be the same width, and the height of your corresponding bars must also be equal, in order for your graph to be correct. C. The statement does not make sense because your bars are twice as wide as the teacher's and twice as tall as the teacher's, so your bar graph is proportional to the teacher's, which is correct. D. The statement does not make sense because the width of the bars in a bar graph does not affect the accuracy of the graph. As long as the width of the bars on your graph represent the same category or interval as the teacher's graph, and the height of your corresponding bars are equal, then your graph is also correct.
D
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. Your pie chart must be wrong, because when I added the percentages on your wedges, they totaled 124%. Choose the correct answer below. A. The statement does not make sense because pie charts are used primarily for relative frequencies, which can add to any total degrees. B. The statement does not make sense because pie charts are used primarily for relative frequencies, which can add to any total percentage. C. The statement makes sense because pie charts are used primarily for relative frequencies, so the total pie must always represent the total relative frequency of 360degrees. D. The statement makes sense because pie charts are used primarily for relative frequencies, so the total pie must always represent the total relative frequency of 100%.
D
Describe possible sources of random and systematic errors in the following measurement. The high temperature of the day in a desert city measured by an outdoor thermometer Choose the correct answer below. A. There will be systematic errors because the thermometer is not meant to be used in the heat of a desert. B. There will be random errors in reading the thermometer because it typically shows very cold temperatures. C. There will be systematic errors in reading the thermometer and possible random errors if the thermometer is not calibrated. D. There will be random errors in reading the thermometer and possible systematic errors if the thermometer is not calibrated.
D
Explain how a graph that shows percentage change can show descending bars (or a descending line) even when the variable of interest is increasing. Choose the correct answer below. A. The horizontal axis on the graph represents unequal intervals such that the drop-off means only the actual value of the variable rises by smaller amounts. B. The horizontal axis on the graph has an opposite direction. C. The vertical axis on the graph has an opposite direction. D. The vertical axis on the graph represents a percentage change such that the drop-off means only the actual value of the variable rises by smaller amounts.
D
For the pair of measurements, state which one is more accurate and which one is more precise. Your true height is 65.60 inches. A tape measure that can read to the nearest one half inch gives your height as 65 and one half inches. A new laser device at the doctor's office that gives readings to the nearest 0.01 inch gives your height as 65.59 inches. Choose the correct answer below. A. The tape measure is both more accurate and more precise. B. The tape measure is more accurate and the laser device is more precise. C. The laser device is more accurate and the tape measure is more precise. D. The laser device is both more accurate and more precise.
D
Give an example in which the absolute error is large but the relative error is small. A. A runner's true weight is 125 pounds, but a scale says he weighs 130 pounds. B. A chemist has 2.9 mg of substance, but a scale measures 2.1 mg. C. A census says that the population of a town is 72,453, but the true population is 96,000. D. A company projects sales of $7.30 billion and true sales turn out to be $7.32 billion.
D
What does the index value of 126.8 in 2000 mean? Explain your reasoning. Choose the correct answer below. A. Gas in 2000 cost 126.8cents per gallon, because the gas price index measures the cost per gallon. B. Gas in 2000 cost 126.8 times as much as gas in 1990, because because the ratio of the gas price index in 2000 to the gas price index in 1990 is 126.8. C. Gas in 2000 cost 1.268cents per gallon, because the gas price index measures the cost per gallon. D. Gas in 2000 cost 1.268 times as much as gas in 1990, because the ratio of the gas price index in 2000 to the gas price index in 1990 is 1.268.
D
What is a frequency table? A. A frequency table is used to display qualitative data. It uses wedges in a circle to represent the relative frequency of each category, which is the number of data values in the category. The size of each wedge is proportional to the relative frequency of the category it represents. B. A frequency table is used to display qualitative data. It uses a set of bars to represent the frequency of each category, which is the number of data values in the category. C. A frequency table has two columns. The first column lists all of the categories of data. The second column lists the frequency of each category, which is the number of data values in the category and all preceding categories. D. A frequency table has two columns. The first column lists all of the categories of data. The second column lists the frequency of each category, which is the number of data values in the category.
D
What is a second way to use percentages? A. Percentages can be used to describe a change in something. For example, out of 34 students, 50% passed the test. B. Percentages can be used to compare two things. For example, out of 945 residents, 80% voted in the last election . C. Percentages can be used to compare two things. For example, the stock dropped 1.5% this past week. D. Percentages can be used to describe a change in something. For example, the cost of milk rose 5% within the past month.
D
What is one way to use percentages? A. Percentages can be used to describe a change in something. For example, out of 3,000 employees, 15% got raises. B. Percentages can be used to describe a change in something. For example, the shoes are 50% lighter, but are 17% more expensive. C. Percentages can be used to express a fraction of something. For example, a company started with 15,000 employees and has grown 3% within the past year. D. Percentages can be used to express a fraction of something. For example, out of 15,000 employees, 3% lost their jobs.
D
What is the purpose of binning? Give an example in which binning is useful. Choose the correct answer below. A. The purpose of binning is to analyze the frequency of qualitative data grouped into categories that cover a range of possible values. A useful example is grouping babies by eye color with 1-point bins. The first bin contains blue-eyed babies, the second bin contains brown-eyed babies, and so on. B. The purpose of binning is to analyze the frequency of quantitative data grouped into categories that cover a range of possible values. A useful example is grouping babies by eye color with 1-point bins. The first bin contains blue-eyed babies, the second bin contains brown-eyed babies, and so on. C. The purpose of binning is to analyze the frequency of qualitative data grouped into categories that cover a range of possible values. A useful example is grouping quiz scores with a maximum score of 40 points with 10-point bins. The first bin contains scores 0-9, the second bin contains scores 10-19, and so on. D. The purpose of binning is to analyze the frequency of quantitative data grouped into categories that cover a range of possible values. A useful example is grouping quiz scores with a maximum score of 40 points with 10-point bins. The first bin contains scores 0-9, the second bin contains scores 10-19, and so on.
D
c. Discuss interesting features of the data revealed by the display. Choose the correct answer below. A. From 1950 to 1980, the percentage of foreign-born citizens remained fairly constant. During the 1980s, the percentage increased. From 1990 to 2010, the percentage was again fairly constant. B. From 1950 to 1990, the percentage of foreign-born citizens increased fairly steadily. From 1990 to 2010, the percentage remained fairly constant. C. From 1950 to 1990, the percentage of foreign-born citizens remained fairly constant. During the 1990s, the percentage decreased. From 2000 to 2010, the percentage was again fairly constant. D. From 1950 to 1990, the percentage of foreign-born citizens remained fairly constant. Starting in the 1990s, the percetnage increased fairly steadily, a trend that continued through 2010.
D
Suppose you want to cut 20 identical boards of length 3 feet. The procedure is to measure and cut the first board, then use the first board to measure and cut the second board, then use the second board to measure and cut the third board, and so on. Answer parts a and b.
a. What are the possible lengths of the 20th board if, each time you cut a board, there is a maximum error of plus or minusone fourth inch? The board could be as short as 31 inches or as long as 41 inches. b. What are the possible lengths of the 20th board if, each time you cut a board, there is a maximum error of plus or minus0.7%? The board could be as short as 31.28 inches or as long as 41.39 inches. HOW TO SOLVE: A: 3x12= 36 36 in.-20 (one fourth in. ) = 31 36+20(1/4) B. 100-0.7=99.3 (36-.993) to 20 power=31.28 36+.993) to the 20 power=41.39
