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- Determine whether the data described below are qualitative or quantitative and explain why.The postal codes of survey The data are qualitative because they don’t measure or count anything
- The brands of peanut butter eaten in households surveyed by a consumer research company.The data are qualitative because they don’t measure or count anything.
- The number of car accidents on a given stretch of highway each year. The data are discretebecause the data can only take on specific values.
- The weights ( in tons) of the trees in a forest. The data are continuous the data can take onany value in an interval.
- Types of movies (drama, comedy, ect.) Nominal
- The cities in a region. Nominal
- A movie with a 4-star rating is twice as good as one with a 2-star rating. The ratio level of measurement does not apply
- The temperatures ( in C) of water samples taken simultaneously in a large are shown below.27. 23.2 22.7 23.9 24.8 27.7 22.4 23.1 25. Are the data qualitative or quantitative? Quantitative - What is the data set’s level Measurement? Interval
- One of the authors received a credit card bill for $3,150, but it included a charge of $1,918 thatwas not valid. Find the values of the absolute and relative errors. The value of the absolute error is $1918. The value of the relative error is 156%.
- 25 people, consisting of a statistics professor and her students, are to measure the length of a room to the nearest 10th^ of a millimeter. Assume that everyone uses the same well-calibrated measuring device, such as a tape measure. The errors are random. If they were systematic, there would be a tendency for the measurements to be all too high or all to low. If the professor wants to minimize the effect of random error in determining the length of the room, isit better to report her own personal measurement as the length of the room or to report the average of all 25 measurements? It is better to use the average because it is likely to be in error by less than most of the individual measurement and it is more reliable than any single measurement. C. Systematic error might result if the tape measure has a manufacturing defectthat made all of the units too small on the tape. D. No, because if there is a systematic error in the measurements, that same error will be present in the average.
- New Vet weight 3278 pounds, Manufactures scale is 10 pounds weight 3284. Transort scale is 0.1 pound and obtains weight 3289.7 pounds. A. The department of trans scale is more precise. B. The manufactures’s scale is more accurate.
A study was conducted of pleas made by 1,028 criminals. Among those criminals, 955 pled guilty, and
393 of them were sentenced to prison. Among the 73 other criminals, who pled not guilty, 51 were sent to
prison. Complete (a) through (d). What percentage of the criminals pled guilty? 92.9% B. What percentage of the criminals were sent to prison? 43.2% C. Among those who pled guilty, what is the percentage who were sent to prison? 41.2% D. Among those who pled not guilty, what is the percentage who were sent to prison? 69.9%
13. Last February there were 717, 367 scheduled passenger flights in a certain country, and in
February of 1995 there were 791,602.
Use a percentage to express the relative change. Use the second given value as the reference
value. Also, write a statement describing the result. The relative difference between February of 1995 and last February is -9%. There is an 9% decrease in the number of scheduled passenger flights from February of 1995 to last February.
- In a certain survey of 1,012 adults, 83% reported having more than one television at home. Find the actual number of respondents corresponding to the given percentage.The number ofadults who reported having more than one television at home is 840
33. When constructing a graph showing the population of two countries, an illustrator draws two
different people with heights proportional to the populations. Identify a way in which the graph might be misleading. What is the general name for such graphs that use drawings of people or objects? Misleading? The graph might be misleading because the aspect of the drawings ofpeople that represent the population of each country could be ambiguous. Viewers of the graph may interpret the area of each person as representing the respective populations. What is the general name for a graph that uses drawings of people or objects? A Pictograph
The accompanying figure shows the highway fuel consumption (mi/gal) for two different models of car. How is the graph misleading? How could it be drawn so that it is not misleading? The graph is misleading
because the vertical axis scale does not start at zero. How could the graph be drawn so that it is not misleading? By starting the vertical scale at 0, the graph will not be misleading.
- The graph shows the percentage change in a price index over 17 years. In what year(s) (of theyears displayed) was the change in the price index the greatest? In what year(s) was the change in the price index the least? How do actual prices in 1991 compare to those in 1990? Based on this graph, what can you conclude about changes in prices during the period shown? 1-1990, 2. 1998 &2002, 3. The actual 1991 prices are about 4.6% higher than those in 1990. 4. Prices have increased in every year, but the increases near the end of the time period are lower than those near the beginning.
- State whether the mean or median would give a better description of the "average" for the measurement below. Explain your reasoning. The mean would give a better description of the "average." For the population of basketball players, there are only a few heights that are extreme, and they are not extreme by very large amounts. In this case, the mean would be better because it takes every height into account.
- Actual times (in seconds) recorded when statistics students participated in an experiment to test their ability to determine when one minute (60 seconds) had passed are shown below. Find the mean, median, and mode of the listed numbers. 55-51-74-65-67-60-49-49…MEAN-58.8, MEDIAN 57.5, A. The mode is 49 sec
- The following table gives the total area in square miles (land and water) of seven states. Complete parts (a) through (c) 1-52,500,2-615,100,3-114,200,4-53,300,5-159,200,6- 104,800,7-5,500- Mean-157800, Median 104800, state-2, New Mean 81583 , New Median79050, state 7, New Mean 183,183, New Median 109,
Suppose you have scores of 70, 75, 80, and 70 on quizzes in a mathematics class. Complete parts (a) through (c). A. 73.75, B. 80, C. NO
38. A student's course grade is based on one midterm that counts as 10% of his final grade, one class
project that counts as 25% of his final grade, a set of homework assignments that countsas 35% of his final grade, and a final exam that counts as 30% of his final grade. His midterm score is 74, his project score is 93, his homework score is 76, and his final exam score is 65. What is his overall final score? His overall final score is 77
39. Find the (a) mean, (b) median, and (c) mode for the given sample data. 3,4,1,2,4,4,1,1,4,3,1,4,3,4. A.
2.8, B. 3.0, C. The mode phenotype code is 4, Do the measureof center make sense? Only the mode makes sense since the data is nominal.
40. 2, left modes, left-skewed, wide variation Suppose you study family income in a random
sample of 300 families. Your results can be summarized as the mean family income was
$45,000, the median family income was $32,000, the highest and lowest incomes were $258,
and 2,400, respectively. C.- HILL 1ST, right-skewed, 150 families, No, because the number of families that earned more than $45,000 depends on the distribution.
- Consider a distribution of the weights of 100 eighth-grade boys.How many modes would youexpect for the distribution? Would you expect the distribution to be symmetric, left-skewed, or right- skewed? D. 1-mode:symmetric
- For the distribution described below, complete parts (a) and (b) below.The ages of 1,000 randomly selected patients being treated for dementia a. How many modes are expected forthe distribution? B. The distribution is probably Trimodal.. A. The distribution is probably left- skewed.
appear to be a difference in variation? Range= 4, Range book 2= 11, Sample 1.7 letters, Sample book 2 3.8 letters, Yes there is much less variation amoung the word lengths in book 1
One of the authors with too much time on his hands weighed each chocolate candy in a bag of 462 plain chocolate candies. Complete parts (a) through (c). A. 5TH, B. 70TH, C. 49TH
- The following data sets give the ages in years of a sample of cars in a faculty parking lot and astudent parking lot at a college. Complete parts (a) through (e).
4-4-4, 7.18-7-9,2-3-4-5-6, 2-5-7-10-11, C. B. – 1.2,3.0,1.0,2.3, YES, A. Because there
are no high or low value outliers. A. the ages of cares in the faculty parking lot are
lower than ages of cars in the student parking lot, and variations in ages of cars in the
faculty parking lot are lower than variation in ages of the cars in the student parking lot.
47.A report claims that the returns for the investment portfolios with a single stock have a standard deviation of 0.55, while the returns for portfolios with 31 stocks have a standard deviation of 0.334. Explain how the standard deviation measures the risk in these two types of portfolios. B. A lower standarddeviation means more certainty in the return and less risk. Hence the return for portfolios with 31 stocks have less risk than the ones with a single stock.
48. The table below shows the batting records of two baseball players in the first half (first
games) and last half of a season. Answer the questions below. JOSH, JOSH, JUDE 49. Polygraph
is 90% accurate A. 220,27,193,87.7 %B. 1740,1737,99.8%
• What is the link between the normal distribution and Video 5: Variation 2 (andEgg
Roulette) , where we relied on statements such as “about two-thirds of observations
are within one standard deviation of the
mean”? egg- good ideal to think about variation as well as averages, and to use thetechnical
terms, you need to report a measure of dispersion as well as a central estimate. 2, if you’re
using the median to describe the central
Estimate of your data, the measure of dispersion you use is the quartiles, the values 25% and 75% of the way along. 3, if you’re using the mean to describe your data set, you have to
calculate using a special formula, something called the standard deviation, as your measure of dispersion. 4th^ if you have the mean and standard deviation, you can work out all sorts of things about your data set. That is using an assumption I’ll tell you about later.
Normal Distribution- there is a connection between coin throw and the results of either natural phenomena, such as how red your blood is, and social phenomena, such as the age at which people decide to run the marathon. And that length is the normal distribution.
Coin throw up a number of random events, what you get is the normal distribution. And of course, many of the phenomena we se around us in the world in general depend on adding up a number of random events. Good example of this would be a body weight depends on genetic factors, such as how you burn fat and your bone structure. Randomly in the population diet, life style factors influcent by friends and family and where you live,. Heads for slow Metabolism, tails if you have a fast metabolism.
The researchers should not be allowed to know who is in the treatment group and who is in the control group.
- In a Gallup poll of 1,
randomly selected
American sportsmenAmerican sportsmen,
89% said that cloning of humans should not be allowed.
Identify the sample, population, and sampling method. Then comment on whether you think it is likely that the sample is representative of the population.
Identify the sample. Choose the correct answer below.
A.
the 1,067 randomly selected American sportsmenAmerican sportsmen This is the correct answer.
Identify the population. Choose the correct answer below.
D.
all American sportsmenAmerican sportsmen
This is the correct answer.
Identify the sampling method. Choose the correct answer below.
B.
Random
Comment on wheather you think it is likely that the sample is representative of the population.
A.
The sample is fairly large and random. Assuming it was obtained by a reputable firm, the sample is likely to be representative of the population.
This is the correct answer.
- Last year's budget for the legislative branch of a certain government was
$4938 million, and this year it is $5355 million. Consider last year's budget of
$4938 million to be the reference value. Complete parts (a) through (d) below.
a. What is the absolute change in the budget from last year to this year?The absolute change in the budget from last year to this year is
million, what is the amount of next year's budget? The amount of next year's budget is
$ 5140.80 million.
- Decide whether the following statement makes sense (or is clearly true) or does not makesense (or is clearly false). Explain your reasoning.
My experiment proved beyond a doubt that vitamin C can reduce the severity of colds, because I controlled the experiment carefully for every possible confounding variable.
Choose the correct answer below.
A.
The statement does not make sense because it is not always easy to discover confounding variables.
- Cluster sampling and stratified sampling both involve selecting subjects in subgroups of the population. What is the difference between those two types of sampling?
Choose the correct answer below.
C.
With cluster sampling, all members of randomly selected subgroups (or clusters) are selected, but with stratified sampling, samples from each of the different subgroups (or strata) are selected.
- What is a sample statistic, what is a population parameter, and what is the difference between them?
What is a sample statistic?
C.
A sample statistic is a numerical value describing some attribute of a sample.
Your answer is correct.
What is a population parameter?
D.
A population parameter is a numerical value describing some attribute of a population.
What is the difference between a sample statistic and a population parameter?
B.
A population parameter is frequently impractical or impossible to find for large populations, however a sample statistic is often easier to find and provides a reasonable approximation to the population parameter.
- The accompanying histogram show the time until failure for a sample of 191 computer chips.Classify the distribution according to its number of modes and its symmetry or skewness. In words summarize the meaning of your results.
report the average of all 25 measurements? Explain. It is better to use the average because it is likely to be in error by less than most of the individual measurement and it is more reliable than any single measurement.
c. Describe any possible sources of systematic errors in the measurement of the room length. Systematic error might result if the tape measure has a manufacturing defect that made all of theunits too small on the tape. d. Can the process of averaging all 25 measurements help reduce any systematic errors? Why or why not? No, Because if there is a systematic error in the measurements, that same error will bepresent in the average.
- Fill in the blank in the following statement. If a truck weights 25% more than a car, then the truck'sweight is _125% of the car's weight.
- The accompanying figure depicts the populations for three regions (A, B, and C). How is thisgraph misleading? How could it be drawn so that it is not misleading? a. How is the graph misleading? The graph is misleading because the horizontal axis scaledoes not start at zero b. How could the graph be drawn so that it is not misleading? By starting the horizontal scale at0, the graph will not be misleading.
- The following table gives the total area in square miles (land and water) of seven states. Complete parts (a) through (c).
State Area
1 52, 2 615, 3 115, 4 53, 5 159, 6 104, 7 5, 900 a. a. 157,943 - 104200 miles b. 2 -81683 mile 78,850 miles c. 7 - 183,283 109,
- The temp of air samples taken simultaneously over a large city are shown. 17.1 16.5 15.918. 18.2 14.6 14.5 14.7 16. Are the data qualitative or quantitative? Quantitative What is the data set’s level of measurement? Interval
- A survey was conducted to determine how employees found their jobs. The accompanying tableand Pareto chart give the successful methods identified by 400 randomly selected employees. Construct a pie chart for these data. Compare the pie chart to the Pareto chart. Can you determine which graph is more effective in showing the relative importance of job sources? A. Pie chart green 18%, blue 14%, red 63%, and yellow 5% B. Is the Pareto chart or the pie chart more effective in showing the relative importance of job sources? The Pareto chart is more effective in showing the relative importance of jobsources by using a vertical scale and arranging the bars in descending order.
21. A data set consists of the 76 ages of women at the time that they won an award in the category ofbest
actress. Complete parts (a) through (c) below. a. One of the actresses was 40 years of age, and she was older than 51 of the other actressesat the time that they won awards. What is the percentile of the age of 40? 67th b. One of the actress was 54 years and 67 and 54? 88th c. 1 of the actress was 60, 68, 60? 89th
at least one source of bias in the study described. Then suggest how the bias might have been avoided. Choose the correct answer below. The researchers may have been more inclined to provide favorable results because funding was provided by a party with a definite interest. The bias could have been avoided if the researchers were not paid by the candy company and the chocolate manufacturers.
26. Suppose that a polygraph is 90% accurate (it will correctly detect 90% of people who are lying and it will
correctly detect 90% of people who are telling the truth). The 1,950 employees of a company are given a polygraph test during which they are asked whether they use drugs. Assume that anyone whom the polygraph operator finds untruthful is accused of lying. Completeparts (a) and (b).
a. 219
b. 27
c. 192
d. 87.7%
e. 1,731 - 1,728 -99.8%
27. Use the following frequency table for the weights (in pounds) of cans 40 of regular coke with binwidth
of 0.0050 pound to construct the corresponding histogram.
Smallblank small 1 inch more 2 inch more high low way low
28. One of the authors received a credit card bill for $2,947, but it included a charge of
$1,717 that was not valid. Find the values of the absolute and relative errors. 1717
29. A mathematician drilled a hole in a die, filled it with a lead weight, and then proceeded to roll it. The
results are given in the following frequency table.
a. 200
b. 139
c. 18%
d. 0.135,0.170,0.205,0.185,0.125,0.
e. 27,61,102,139,164,
- Blood alcohol concentrations of drivers involved in fatal crashes and then given jail sentences are listed below. Find the range and standard deviation. 0.28,0.18,0.18,0.15,0.13,0.22,0.31,0.22,0.14,0.15,0.12,0.15 RANGE=0.190 Standard=0.
31. What is the distinction between qualitative data and quantitative data? Give a few examples ofeach.
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.
32. A professor records the following final grades in one course. Construct a frequency table for the
grades.AAAAAA,BBBBBB,CCCCCCCC,DDDD,F
A. 5-20.8%-
B. 6-25%-
C. 8-33.3%-
D. 4-16.7%-
E ...1-4.2%
F. 24-1-
