AP Stat

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In order to plan the design of a school spirit shirt, the student council conducted a survey. They asked students which color they prefer (blue, white, maroon) and which type of shirt (t-shirt, sweatshirt). The table summarizes the responses. t-shirtsweatshirttotalblue251035white151530maroon51015total453580 What percent of the students prefer a blue sweatshirt?

12.5

The center of a histogram...

is the point in the graph where about half of the data lies above and half of the data lies below.

Twelve babies spoke for the first time at the following ages (in months):15 26 10 9 15 20 18 11 8 20 12 13 Find the mean and median and indicate which is which.

mean: 14.75 median:14

Does regular exercise decrease the risk of cancer? A researcher finds 200 women over 50 who exercise regularly, pairs each with a woman who has a similar medical history but does not exercise, then follows the subjects for 10 years to see which group develops more cancer. This is a ...

prospective study

Bias can be controlled in surveys by all of the following except one. Choose the one option that will not control bias.

Prompting respondents so that they give correct responses.

Vocabulary:Two variables that are actually not related to each other may nonetheless have a very high correlation because they both result from SOME OTHER, possibly HIDDEN, factor. This is an example of ...

a lurking variable.

Ch11_16A person with type O-positive blood can receive blood only from other type O donors. About 44% of the U.S. population has type O blood. At a blood drive, how many potential donors do you expect to examine in order to get three (3) units of type O blood?

between 6 and 10

Chapter 3 Exercises #24 These percentages are ...

column percentages

A residual plot that indicates the model provides an appropriate description of the data ...

has no pattern

As a 4-H project, Billy is raising chickens. He feeds and waters them evey day, and collects the eggs every other day, selling them to people in the neighborhood. He has found that each hen's nest will contain from 0 to 2 eggs. Based on past experience he estimates that there will be no eggs in 10% of the nests, one egg in 30% of the nests, and 2 eggs in the other 60%. Conduct a simulation to estimate how many nests Billy will have to visit to collect a dozen eggs.1) Describe how you will use a random number table to conduct this simulation. 2) Give your results for three trials using the random number table below. 37542 04805 64894 74296 24805 24037 20636 10402 00822 9166508422 68953 19645 09303 23209 02560 15953 34764 35080 3360699019 02529 09376 70715 38311 31165 88676 74397 04436 2765912807 99970 80157 36147 64032 36653 98951 16877 12171 768333) State your conclusion after performing 3 trials.

1) To use a random number table you would have to pick certain numbers to represent each possibility. The numberss picked have to have the same possibility of happening as the situation you match them to. 0 will represent getting zero eggs; 1,2 and 3 will represent getting one egg; and 4,5,6,7,8, and 9 will represent getting two eggs. This is a reasonable assignment because for zero eggs, out of ten, one number has a .1 probability of being picked (this makes sense for the other two possibilties as well). 2) In the first trial, Billy had to visit 7 nests. In the second trial, Billy had to visit 10 nests. In the third trial, Billy had to visit 7 nests. 3) In conclusion, Billy will, on average, need to visit about 8 nests in order to collect a dozen eggs. This can be found by averaging the three trials.

A survey of autos parked in student and staff lots at a large university were classified by country of origin, as seen in this table.Country of Origin DRIVER Student StaffAmerican 94 81European 38 22Asian 66 53What percent of the European car drivers were students?

63%

You are conducting an experiment to test the density of a new recipe for chocolate cake. You will test the recipe with 3 different baking temperatures (350, 400 and 450) and 3 different baking times (45 minutes, 55 minutes and 60 minutes). How many treatments are there?

Listed below are 10 of the students in your class. Use the random numbers listed to choose a random sample of 3 of them. Clearly explain your method.Lucy, Charlie, Cindy, Bobby, Jan, Marcia, Peter, Greg, Oliver, Arnold04905 83852 29350 91397 19997 65142 05087 11232

First you assign each student a number 00-09 (going down the row). So as you go through the samples you can pick the classmates. In the first sample set you get 04 and 05 which correspond with Bobby (04) and Jan (05). You then have to wait until the end of the third sample and the beginning of the next one to get 09 which corresponds with Oliver.

convenience

Have each council member survey 50 friends, neighbors, or co-workers.

simple (SRS)

Have the Board of Elections assign each voter a number, then select 400 of them using a random number table.

In order to rate TV shows, phone surveys are sometimes used. Such a survey might record several variables, some of which are listed below. Which of these variables are categorical? I. The type of show being watched II. The number of persons watching the show III. The ages of persons watching the show IV. The name of the show being watched V. The number of times the show has been watched in the last month

I and IV

Occasionally when I fill my car with gas, I figure out how many miles per gallon my car got. I wrote down those results after 6 fill-ups in the past few months. Overall, it appears my car gets 28.8 miles per gallon.What PARAMETER am I trying to estimate?

I think it is: mean gas mileage for the vehicle

I think it is: prospective study

Which of the following statements are true? I. A histogram is exactly the same as a bar graph. II. Stem plots preserve the actual data values. III. Categorical data can be shown using a stem plot.

Which of the following are true statements? READ THESE STATEMENTS VERY CAREFULLY and select all that are TRUE. I. Voluntary response samples often underrepresent people with strong opinions. II. Convenience samples often lead to undercoverage bias. III. Questionnaires with nonneutral wording are likely to have response bias.

II and III

A basketball player has a 70% free throw percentage. Which plan could be used to simulate the number of free throws that the player will likely make in the next five free throw attempts? Select all that apply.1. Let 0,1 represent making the first shot, 2 and 3 represent making the second shot,....8 and 9 represent making the fifth shot. Generagte five random numbers 0-9, ignoring repeats.II. Let 0,1,2 represent missing a shot and 3,4,...9 represent making a shot. Generate five random numbers 0-9 and count how many numbers are in the range of 3-9.III. Let 0,1,2 represent missing a shot and 3,4,....9 represent making a shot. Generate five random numbers 0-9 and count how many numbers are in the range of 3-9, ignoring repeats.

II only

The Mars candy company starts a marketing campaign that puts a plastic game piece in each bag of M&Ms. 25% of the pieces show the letter "M," 10% show the symbol "&," and the rest just say "Try again." When you collect a set of three symbols "M," "&," and "M" you can turn them in for a free bag of candy. About how many bags will a consumer have to buy to get a free one? Let's use a simulation to find out.Explain how you will use the random numbers listed below to conduct your simulation. 57821 76309 63508 29418 13026 34993 54636 17877 00987 23401

Incorrect answer: In this case you will assign them values fromm 00-99. Numbers 00-24 will represent an M and values 25-34 will represent the &. The rest of the numbers (35-99) will represent the try again outcome. In the simulation, you will need to buy about 24 bags of M&Ms before you get the entire set and a free one.

Ch12_11cIn a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan. They decide to send a survey home with every student, and ask parents to fill it out and return it the next day.

It should be unbiased because of stratified sampling

Chapter 7 Exercises #19 part c Does the assocation shown in the scatter plot and describe by a correlation of .74 prove that more fans will attend games for winning teams?

No...even a very strong association does not guarantee a result

Administrators at a hospital are concerned about the possibility of drug abuse by people who work there. They decide to check on the extent of the problem by having a random sample of the employees undergo a drug test. Several plans for choosing the sample are proposed. NAME the correct TERM to describe the sampling strategy.Each employee has a 4-digit ID number. Randomly choose 40 numbers.

SRS

A statistics student properly simulated the number of students at her high school who have the flu. She then reported, "The number of students at this school with the flu is 40."What is wrong with this conclusion?

The conclusion should indicate that the simulation suggests that there are 40 students at the school who have the flu. Actual results might not match the simulated results exactly.

Chapter 3 Exercises #8b What is true about the percentages listed?

The percentages total more than 100%.

Ch13_12In 2001 a report in the Journal of the American Cancer Institute indicated that women who work nights have a 60% greater risk of developing breast cancer. Researchers based these finding on the work histories of 763 women with breast cancer and 741 women without the disease.This is a study and not an experiment.

True

Ch13_6To research the effects of "dietary patterns" on blood pressure in 459 subjects, subjects were randomly assigned to three groups and had their meals prepared by dieticians. Those who were fed a diet low in fat and cholesterol and high in fruits, vegetables, and low-fat dairy foods lowered their systolic blood pressure by an average of 6.7 points when compared with subjects fed a control diet.True or False.This is an experiment.

True

Chapter 4 #14 The type of graph pictured is ________________Select the BEST answer choice to describe the distribution. OBSERVE THE STEMS!!!

back to back stem plot with split stems

Chapter 2 Exercises #15 In this context the country of origin is what type of variable?

categorical

Administrators at a hospital are concerned about the possibility of drug abuse by people who work there. They decide to check on the extent of the problem by having a random sample of the employees undergo a drug test. Several plans for choosing the sample are proposed. NAME the correct TERM to describe the sampling strategy.Randomly select a department (say, radiology) and test all the people who work in that department - doctors, nurses, technicians, clerks, custodians, etc.

cluster

Ch12_6Hoping to learn what issues may resonate with voters in the coming election, the campaign director for a mayoral candidate selects one street from each of the city's election districts. Staff members go there and interview all the residents they can find.Selecting one street from each district and sampling within that street is an example of a ______________

cluster sample

Twelve babies spoke for the first time at the following ages (in months):15 26 10 9 15 20 18 11 8 20 12 13Based ONLY on the values of the mean and the median, what can you say about the shape of the distribution of the data set? Explain!

mean- 14.75median- 14 Because the mean is greater than the median, it can be infered that the data is skweed right. The pattern of right skewed data includes a median which is less than the mean.

Ch12_10Dairy inspectors visit farms unannounced and take samples of the milk to test for contamination. If the milk is found to contain dirt, antibiotics, or other foreign matter, the milk will be destroyed and the farm re-inspected until purity is restored.What is the population PARAMETER of interest?

proportion of samples passing inspection

systematic

Call every 500th person in the phone book.

Administrators at a hospital are concerned about the possibility of drug abuse by people who work there. They decide to check on the extent of the problem by having a random sample of the employees undergo a drug test. Several plans for choosing the sample are proposed. NAME the correct TERM to describe the sampling strategy.At the start of each shift, choose every tenth person who arrives for work.

Incorrect answer: systematic

stratified

Randomly pick 50 voters from each election district.

(60+119)/354

A company manufactures polypropylene rope in six different sizes. To assess the strength of the ropes they test TWO samples (1 and S2) of each size to see how much force (in kilograms) the ropes will hold without breaking. The table shows the results of the tests. We want to create a model for predicting the breaking strength from the diameter of the rope. Diameter (mm) Strength (kg)S1 S2 4 60 76 7 157 153 10 254 262 12 334 388 15 551 529 20 938 893 AVERAGE the two samples' response variable values to create the needed response variable.Use the (logx, logy) transformation to straighten the scatterplot and state the appropriate model (equation).

(logx, logy) power model on (4,68) (7,155) (10,258) (12,361) (15,540) (20, 915.5) results in yhat = (6.93)(x^1.61) strength of rope = (6.93)(diam^1.61)

Ch 11_4Many kinds of low tech board games people play rely on randomness. (These are not video games.)Cite three (3) different methods commonly used in athe attempt to achieve this randomness, and disucss the effectivenesss of each.

- Shuffling is used in card games in order to assure that the cards you receive have no predetermined possibilities, this creates fixed random events. - Coin flips and dice rolls in bets or random assignments make it so that there is no possibility of knowing the outcome. - Random inputs in games by adding more inputs to choose from results in more variables to consider.

-.949

Suppose you are analyzing the relationship between the number of hours worked per day and the number of sick days used each month. Here is the regression analysis.Dependent variable: # of sick days used in the monthR-squared = .947s = 14.7Variable CoefficientConstant 2.1# of hrs. per day 0.0531n = 100What is the correlation between number of hrs. worked per day and number of sick days used in the month?

.97

Ch10_2dWhat is the answer to part d?

0.77

Ch13_18Weight is an issue for both humans and their pets. A dog food company wants to compare a new lower-calorie food with their standard dog food to see if it is effective in helping inactive dogs maintain a healthy weight. They have found several dog owners willing to participate in the trial. The dogs have been classified as small, medium, or large breeds, and the company will supply some owners of each size of dog with one of the two foods. The owners have agreed not to feed their dogs anything else for a period of 6 months, after which the dogs' weights will be checked.HOW MANY TREATMENTS ARE BEING USED???

Students in a political science course were asked to describe their politics as "Liberal", "Moderate", or "Conservative." Here are the results: Liberal Moderate ConservativeFemale 38 41 11Male 51 48 20What are the MARGINAL DISTRIBUTIONS by gender? Remember that these are reported as percents.

90/209 = 43% females, 119/209 = 57% males

x 2 5 6 8 10y 5 27 35 65 102 Find both an exponential and power model for this data.Which model is the MOST appropriate for the data?Justify your answer

A power model; this is because the r for the power model is .9992 and round up to 1, whereas the exponential model has an r of .98, which is still high, just not as high as the power model.

We say that the design of a study is biased if which of the following is true? Select the answer that comes closest to the general definition of bias.

Actions are taken that systematically favor certain outcomes.

Kerry is a systems manager for a large company. In his work, he has found that about 5% of all CDs he orders are bad. He needs to give one of the executives at his company five good CDs. Plan, but do not carry out, a simulation to estimate how many CDs Brian will have to check to get five good CDs for the executive. Describe the random number assignment and how you will use a random number table to conduct this simulation.

Brian will have to assign random numbers to the different possibilities. In this case numbers 0-19, with 0 being a bad CD and the rest being good CDs. She can do this in sets of 5 to get easier counts of 20 CDs (because logically 1 in every 20 CDs is bad). Therefore he will only really need to inspect about 20 CDs.

Give two major differences between the mean and median as measures of the center of the distribution.

Graded Mean commes from avergaing all of the numbers in the data, this means that it will factor in outliers. So, if there is an outlier, the mean will not be an accurate measure of center. Whereas, median represents the middle of the data and will most likely not refelect the outlier in its value. The second major difference is that when the data is skewed you cannot use mean as it is not representative of the data, rather you would use the median value.

The body temperature of students is taken each time a student goes to the nurse's office. The five number summary for the temperatures of students on a particular day is 96.6 - 97.85 - 98.25 - 98.6 - 101.8.After the data were picked up in the afternoon, three more students visited the nurse's office with temperatures of 96.7 - 98.4 - 99.2. Were any of these outliers? Explain.RECALL that none of the numbers in the five number summary can be considered outliers...any other value beyond the fences is an outlier.

Graded The fences for the data are placed at 96.725 and 99.725. This means that the only outlier that came from the three students which visited the nurse's office in the afternoon is 96.7, as it falls bellow the fences. The fences are calcualted with Q1-(1.5*IQR) and Q3+(1.5*IQR) or in this case...97.85-1.125=96.725 and 98.6+1.125. (1.125 comes from multiplying 1.5 by the IQR which is 98.6-97.85=.75)

Chapter 2 Exercises#12 Which of these variables are quantitative? I. age II. days absent III. current grade level

I and II

Which statement about influential points MUST be true?I. Removal of an influential point changes the slope of the regression line.II. Data points that are outliers in the horizontal direction are more likely to be influential than points that are outliers in the vertical direction.III. Influential points will always have large residuals.

I and II only

Criticize the following simulation:A student assigns a random number from 1 to 13 to simulate the value of a card drawn at random from a standard deck of playing cards.

I think it is: The simulation should model the real situation.

Ch12_14dGiven humanity's great tradition of exploration, do you favor continued funding for space flights?

IDK answer

Which statment(s) is/are true? I. Random scatter in the residuals indicates a model with high predictive power. II. If two variables have a very strong linear relationship, then the correlation between them will be near +1.0 or -1.0. III. The higher the correlation between two variables the more likely the association is based in cause and effect.

II only

The Mars candy company starts a marketing campaign that puts a plastic game piece in each bag of M&Ms. 25% of the pieces show the letter "M," 10% show the symbol "&," and the rest just say "Try again." When you collect a set of three symbols "M," "&," and "M" you can turn them in for a free bag of candy. About how many bags will a consumer have to buy to get a free one? Let's use a simulation to find out. (This is the second part to a question you may have already had)Carefully conduct and label your simulation using the digits provided, show your results, and state your conclusion.57821 76309 63508 29418 13026 34993 54636 17877 00987 23401

Incorrect answer: 00-24 is M, 25-34 is & and 35-99 is Try Again (TA). [57]TA[82]TA[17]M[63]TA[09]M[63]TA[50]TA[82]TA[94]TA[13]M[02]M[63]TA[49]TA[93]TA[54]TA[63]TA[61]TA[78]TA[77]TA[00]M[98]TA[72]TA[34]& ~ This mean that you would have to buy 24 bags of M&Ms in order to complete the M&M and get a free bag.

Ch 11_10Cereal Problem Again...Suppose you really want the Tiger Woods picture card. How many boxes of cereal do you need to buy to be pretty sure of getting at least one? Your simulation shold use at least 10 runs. Include a short explanation of your method.

Incorrect answer: You need to buy atleast 10 cereal boxes. I found this by using the random number generator on my calculator and assigned number 0-9 to each person. I then ran the simulation 10 times and out of all of these there were only two times in which Tiger Woods' numbers were present so I assumed that to be safe that you get a Tiger Woods card, it is best to buy 10.

A medical researcher finds that the more overweight a person is, the higher his blood pressure tends to be. That is not very specific but we can say something about ONE of the following descriptors, FORM, DIRECTION, or SHAPE.What do we know about the correlation between weight and blood pressure?

It is a positive correlation, because as weight increases so does blood pressure.

Ch8_29cExplain what the slope of the line means in this problem.

It means that at every minute, it adds .44 minutes of analog time.

Twelve babies spoke for the first time at the following ages (in months):15 26 10 9 15 20 18 11 8 20 12 13 Find the five number summary. Identify each value with number AND statisical name.

Min- 8 Q1-10.5 Median- 14 Q3- 19 Max- 26

Ch13_26bRecently, a group of adults who swim regularly for exercise were evaluated for depression. It turned out that these swimmers were less likely to be depressed than the general population. The researchers said the difference was statistically significant.Is this an experiment or an observational study?EXPLAIN.

Observational. This is because there was nothing being added to test, it was just observinng thoe who already swam regularly.

Ch13_8Is diet or exercise effective in combating insomnia? Some believe that cutting out desserts can help alleviate the problem, while others recommend exercise. Forty volunteers suffering from insomnia agreed to participate in a month-long experiment. Half were randomly assigned to a special no desserts diet while the others continued desserts as usual. Half of the people in each of these groups were randomly assigned to an exercise program and the others were told not to exercise. Those who ate no desserts and engaged in exercise showed the most improvement.Identify the population of interest.

People suffering from insomnia.

cluster

Randomly select several city blocks; interview all the adults living on each block.

The stemplot displays the 1988 per capita income (in hundreds of dollars) of the 50 states. Which of the following best describes the data?

Skewed distribution, mean greater than median

Teacher A's pre-calculus class had a standard deviation of 2.4 on a trigonometry test, while Teacher B's pre-calculus had a standard deviation of 1.2 on the same test. What can be said about these two classes?

Teacher B's class is more homogeneous than Teacher A's class.

Criticize the following simulation:A student assigns a random number from 1 to 13 to simulate the value of a card drawn at random from a standard deck of playing cards.

The simulation should model the real situation.

Name and describe the kind of bias that might be present if the adminstration of a hospital decides that instead of subjecting people to random testing they'll just interview employees about possible drug abuse.

The type oe bias that would be present would be response bias because the employees might lie about the drug abuse or they also have the choice not to participate at all in the survey.

Which variable is NOT quantitative?

The types of cars in the parking lot.

The City Council decides to conduct a telephone poll. Pollsters ask a carefully chosen random sample of adults this question: "Do you favor the construction of a new prison to deal with the high level of violent crime in our State?"In what way might the proportion of "Yes" answers fail to accurately reflect true public opinion? Explain briefly. What kind of bias is this?

The way in which the question is worded would you sway the public to answer use because of the key word "violent crime". This would result in response bias.

Administrators at a hospital are concerned about the possibility of drug abuse by people who work there. They decide to check on the extent of the problem by having a random sample of the employees undergo a drug test. Several plans for choosing the sample are proposed. Name the sampling strategy.Explain why sampling an entire department, might be biased. Be sure to name the kind(s) of bias you desribe.

This is an example of cluster sampling which can result in an underrepresentation of the entire hospital. The type of bias would be undercoverage, as not every type of person might be covered in this sampling.

Listed below are names of the 20 pharmacists on the hospital staff. Use the random numbers listed to select three of them to be in the sample. Clearly explain your method.Pastore, Back, Spiridonov, Ahi, Hedge, MacDowell, Schissel, Novelli, Lavine, Kaplan, Highland, Roundy, Grubb, Markowitz, Glass, Davies, Golkowski, Reeves, Janis, Yen04905 83852 29350 91397 19997 65142 05087 11232

This will be done by numbering the pharmacists 00-19. So each one of these numbers will represent a pharmacist. Therefore if you go through these numbers then you can randomly select the pharmacists, for example 04 in the first set represents Hedge (as it was the number correspondong to them). Then you can pick 09 from the end of set 3 and beginning of set 5, this represents Kaplan. The last one you can also pick is 13 which is right next to 09 and represents Markowitz.

quantitative data

always have units

variable

an attribute or characteristic of an object whose value varies from case to case

Chapter 7 Exercises #11 Which scatterplot is best described as having a correlation factor of -.487?

categorical data

describes data by labels

Ch12_1A business magazine mailed a questionnaire to the human resource directors of all of the Fortune 500 companies, and received responses from 23% of them. Those responding reported that they did not find that such surveys intruded significantly on their workday.Identify the population PARAMETER of interest.

proportion of human resource directors who don't feel surveys intruded on their work day

Twenty dogs and twenty cats were subjects in an experiment to test the effectiveness of a new flea control chemical. It is suspected that cats and dogs may react differently to the new chemical and this is considered in the design of the experiment.Ten of the dogs and 10 of the cats were randomly assigned to an experimental group that wore a collar containing the chemical, while the others wore a similar collar without the chemical. After 30 days veterinarians were asked to inspect the animals for fleas and evidence of flea bites. This experiment is ...

randomized block, blocked by species

bar chart

shows a count for each category

Chapter 4 Exercises #15 The SHAPE of this hurricane data distribution is _______

skewed right

Administrators at a hospital are concerned about the possibility of drug abuse by people who work there. They decide to check on the extent of the problem by having a random sample of the employees undergo a drug test. Several plans for choosing the sample are proposed. NAME the correct TERM to describe the sampling strategy.There are four employee classifications: doctors, medical staff (nurses, technicians, etc.), office staff, and support staff (custodians, maintenance, etc.).Randomly select ten people from each classification.

stratified

Ch12_11dIn a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan. They decide to randomly select 20 parents from each elementary school. Send them a survey, and follow up with a pone call if they do not return the survey within a week. NAME the specific sampling strategy being used by the PTA.

stratified sample

data

systematically recorded information

Vocabulary:Residuals are ...

the difference between observed responses and values predicted by the model.

Ch13_34aCan special study courses actually help raise SAT scores? One organization says that the 30 students they tutored achieved an average gain of 60 points when they retook the test.Explain why this does not necessarily prove that the special course caused the scores to go up.

this does not prove that the special course caused the scores to go up because the students were not randomly assigned. Those who signed up for the course could have been special or had some other background.

Chapter 3 Exercises #5b What percent of deaths were from causes not listed in the table?

26.3%

All students in the physical education class completed a basketball free-throw shooting event and the highest number of shots made was 32. The next day a student transferred into the school and completed the event, making 40 shots. Indicate whether adding the new student's score to the rest of the data made each of these summary statistics increase, decrease, or stay about the same. THINK ABOUT THE INTENT OF THE QUESTION.a. meanb. medianc. ranged. IQRe. standard deviation

The new student would cause the mean to increase.The new student would not cause the median to increase or decrease.The new student would cause the range to increase.The new student would caus the IQR to increase.The new student would cause the standard deviation to increase.

The following table shows the number of hot dogs eaten by contestants in a hot dog eating contest in 2005. James 45 Susan 20 Maggie 28 Richard 15 Wes 56 Amy 48 Daniel 36 What type of display would you use to display this data? Don't forget that the names are also a variable.Defend your choice.

I would use a histogram to best display this data. When looking at the data in a histogram, it is easy to observe which indivdual ate the most hot dogs in the contest. A histogram would be able to have every contestant's name labeled and accurately show how much they ate in comparison to the other contestants.

Chapter 3 Exercises #12Although the pie chart looks appropriate, it has many flaws. I. total is not 100% II. no variables are named III. sizes do not accurately reflect the % Which of these are flaws in the data display?

I, II, and III

We might choose to display data with a stemplot rather than a boxplot because a stemplot ... I. reveals the shape of the distribution II. is better for large data sets III. displays the actual data

III only

Chapter 3 Exercises #15d What percent of the white graduates are planning to attend a 2-year college?

13.4%

Students in a political science course were asked to describe their politics as "Liberal", "Moderate", or "Conservative." Here are the results: Liberal Moderate ConservativeFemale 38 41 11Male 51 48 20What percent of the class considers themselves to be "liberal"?

42.6%

Here are the weights (in pounds) of 20 steers on an experimental feed diet:183 140 136 142 172 153 172 156 70 167 192 166 113 171 159 129 112 135 174 155Make a stemplot of this data.

7| 0 8| 9| 10| 11| 2 3 12| 9 13| 5 6 14| 0 2 15| 3 5 6 9 16| 6 7 17| 1 2 2 4 18| 3 19| 2

As reported in the Journal of the American Medical Association (June 13, 1990), for a study of ten nonagenarians (90+yrs old), the following data shows a measure of strength versus a measure of functional mobilityStrength (kg) 7.5 6 11.5 10.5 9.5 18 4 12 9 3Walk time (s) 18 46 8 25 25 7 22 12 10 48Find the LSRL and tell what the slope signifies?

The sign is negative, signifying that the greater the strength, the less the functional mobility.

Chapter 7 Exercise #5 Describe the association in scatterplot labeled #2.

moderate association

# of seeds

The coefficient of determination for the scatter plot pictured is approximately...(More than one answer may apply)

0.88

Chapter 4 Exercises #11 Which of the following statements is true about the stemplot pictured in the question. I. contains a gap II. skewed right III. outliers are present IV. symmetric

1, II, and III

Ch8_35eThe hardness of Derby's municipal water is about 100 ppm of calcium.Use the equation suggested by the computer printout to predict the mortality rate in Derby.

1,353 (per 100,000)

Suppose you are analyzing the relationship between the number of hours worked per day and the number of sick days used each month. Here is the regression analysis.Dependent variable: # of sick days used in the monthR-squared = 94.7s = 14.7Variable CoefficientConstant 2.1# of hrs. per day 0.0531n = 100How many observations were used in this analysis?

100

Doctors studying how the human body assimilates medication inject some patients with penicillin, and then monitor the concentration of the drug (in units/cc) in the patients' blood for several hours. The data are shown in the table.Time Elapsed Concentration(Hours) (Units/cc) 1 42 2 28 3 19 4 13 5 9 6 6 7 4First they tried to fit a LINEAR model. The regression analysis is shown.Regression of Concentration on Time ElapsedDependent Variable: ConcentrationR-squared = 90.05%Variable Coeff S.E. of CoeffConstant 41.2857 2.1602Time -6 1.8766Not being satisfied with those results the researchers try a new model, using the reexpression log(Concentration). Examine the regression analysis below.Dependent Variable: log (Concentration)R-squared = 99.98%Variable Coefficient S.E. of CoefficientConstant 1.7891 0.045Time -0.1688 0.010Is this model better than the original linear model? Why or why not?Using the new nonlinear model, estimate the concentration of penicillin after 4 hours....remember the transformation used is x, logy

The mean age of 12 of the members attending a mathematics department faculty meeting is 37. Mr. Smith, who is 50, arrives late. What is the average of all 13 members?

52%

In order to plan the design of a school spirit shirt, the student council conducted a survey. They asked students which color they prefer (blue, white, maroon) and which type of shirt (t-shirt, sweatshirt). The table summarizes the responses.What are the MARGINAL Distributions by shirt type? Remember these should be reported as percents. t-shirtsweatshirttotalblue251035white151530maroon51015total453580

56.25% t-shirt, 43.75% sweatshirt

Foresters use regression to predict the volume of timber in a tree using easily measured quantities such as diameter. Let y be the volume of timber in cubic feet and x be the diameter in feet (measured at 3 feet above ground level). One set of data gives y = -30 +60x. The predicted volume for a tree of 18 INCHES is:

60 cubic feet

66.7%

It's easy to measure the circumference of a tree's trunk, but not so easy to measure its height. Foresters developed a model for ponderosa pines that they use to predict the tree's height (in feet) from the circumference of its trunk (in inches): height = 1.46 (circumference) + 5A lumberjack finds a tree with a circumference of 60 inches. How tall does this model estimate the tree to be? (Round to the nearest whole number)

93'

Given the least-squares regression line: [Cost of a Monopoly Property] = 67.3 + 6.78 * [Spaces From GO],FIND the residual for Reading Railroad which costs $200 and is 5 spaces from GO.

98.8

Describe, in words, how a strong negative scatterplot would look. If the scatterplot is not possible, say so.

A strong negative scatterplot would have a linear appearance, going in a negative direction with very little sparsity in the data points.

An agriculture research firm is testing a new type of technique for growing plants. They keep track of the number of seeds in each plot and the number of healthy plants that grow for the plot. The data is given in the table. # of seeds5045535147# of healthy plants2319222019 What is the equation for the Least Squares Regression Line obtained from the calculator?

Enter #seeds into L1Enter # healthy plants into L2Stat/Calc/LinRegy = a + bxusing the a and b from the result

This question will be graded using the AP FR Scoring Guidelines.A psychologist counsels people who are getting divorced. A random sample of six patients provided the following data where x= number of years of courtship before marriage and y = number of years of marriage before divorce.x 3 .5 2 1.5 5y 9 6 14 10 20 Use your calculator to determine the least-squares regression line (LSRL). Be sure to identify the variables by name.What is the correlation factor (r) between x and y? Interpret the number.What is the coefficient of determination (r^2) between x and y? Interpret the number.Find the residual for the first data point and tell how you found it.

Graded * number of years of marriage before divorce= 5.36+2.68(number of years of courtship before marriage) * r=.85; This is a strong positive correlation which means there is a pretty good relationship between years of courtship and years of marriage. * r^2=.72; This is a little less than a strong positive correaltion which means that this relationship is best represented and has a stronger correlation in a linear model. * residual= -4.4; In order to get this I plugged in the number 3 to the equation I provided in my first bullet which gave me the value of 13.4 years of marriage as the predicted value. I then subtracted the observed value,9, from the predicted value, 13.4, and got -4.4.

What is true of a data distribution having the BULK of the data at the lower numbers? I. The distribution is skewed to the right. II. The mean is smaller than the median. III. We should summarize with mean and standard deviation.

I only

Here are the weights (in pounds) of 20 steers on an experimental feed diet: 183 140 136 142 172 153 172 156 70 167 192 166 113 171 159 129 112 135 174 155 Where is the center of the distribution of this data set?

The median of this data set is at 155.5. You would use median for the center given that when ploteed, this data is skewed left. When your data is skewed, you employ median as opposed to mean.

Students in a political science course were asked to describe their politics as "Liberal", "Moderate", or "Conservative." Here are the results: Liberal Moderate ConservativeFemale 38 41 11Male 51 48 20Do gender and political tendencies appear to be related? Explain.

YES...45.5% (41/90) Females are moderates while 40.3% (48/119) of males are moderates

Ch9_6aDoes the value of rsquare mean that a LINEAR model is NOT appropriate.EXPLAIN completely!!

Yes the value of rsquare can demonstrate that a linear model is not appropriate. In some cases, when the shape is curved, it can show as having a very low coorealtion. This does not mean that the data does not display any type of relationship or pattern it just is not a linear realtionship which is shown.

statistic

a numerical summary of data

A simple random sample of adults living in a suburb of a large city was selected. The age and annual income of each adult in the sample were recorded. The resulting data are summarized in the table below. Annual Income Age Category 25,000-35,000 35,001-50,000 Over $50,000 Total 21-30 8 15 27 50 31-45 22 32 35 89 46-60 12 14 27 53 Over 60 5 3 7 15 Total 47 64 96 207 a) What is the probability that a person chosen at random from those in this sample will be in the 31-45 age category?b) What is the probability that a person chosen at random from those in this sample whose incomes are over $50,000 will be in the 31-45 age category? Show your work.c) Based on your answers to parts (a) and (b), is annual income independent of age for those in this sample? Explain.

a) There is a probability of 43% that a random person chosen is in the 31-45 age category. b) There is a 36.46% chance of picking a 31-45 year old from those whose incomes are over $50,000. (Work: Those with an icome over $50,000= 96; in this column there are 35 individuals who are in the 31-45 age category. Then you take 35/96 and multiply by 100 to get the percent of 34.46%). c) Based on this sample, it can be inferred that it is slighlt more likely to make more income if youu are older but there are also just as many 21-30 year olds as there are 46-60 year olds who make over $50,000, so it is not a concrete relationship.

Chapter 3 Exercises #13b Which graph type works better for this specific data,bar graph or pie chart? Explain.

bar graph because it makes comparisons easier

List the variables. Indicate whether each variable is categorical or quantitative. If the variable is quantitative, tell the units. In June 2003 Consumer Reports published an article on some sport-utility vehicles they had tested recently. They reported some basic information about each of the vehicles and the results of some tests conducted by their staff. Among other things, the article told the brand of each vehicle, its price, and whether it had a standard or automatic transmission. They reported the vehicle's fuel economy, its acceleration (number of seconds to go from zero to 60 mph), and its braking distance to stop from 60 mph. The article also rated each vehicle's reliability as much better than average, better than average, average, worse, or much worse than average.

brand of each vehicle (categorical), price (quantitative- dollars), whether it had a standard or automatic transmission (categorical), fuel economy (categorical), acceleration (m/s2), braking distance to stop from 60mph (quantitative- m) and vehicle reliability (categorical)

density of the cake

A scatterplot x versus log y shows a strong positive LINEAR pattern although the original data do not.Which type of non-linear model (exponential or power) would be appropriate for the original data?

exponential

We collect these data from 50 male students. Which variable is categorical?

eye color

A company's sales grow by the SAME FIXED AMOUNT each year. That means the increase is the same year over year. This growth is ...

linear

Chaper 3 Exercises #29d What were the delay rates at the SMALL hospital for each kind of surgery?

major: 20% minor: 8%

Ch8_21dComputer Software says that rsquare = 0.894, what is the correlation between age and price?

r=-.9455

Chapter 2 Exercises #2 The HOW of this question is____________

sampling

pie chart

shows a proportion for each category

The table below shows how a company's employees commute to work. Transportation Car Bus TrainManagers 26 20 44Labor 56 106 168What kind of display would be best to demonstrate an association, or not, between job classification and method of transportation?

side by side segmented bar graphs

Environmental researchers have collected rain acidity data for SEVERAL DECADES. They want to see if there is any evidence that attempts to reduce industrial pollution have produced a TREND toward less acidic rainfall. They should display their data in a(n)

timeplot

Chapter 4 Exercises #3 part c How did you describe the variable for this distribution?

uniform, symmetric

Ch 11_18A new electronics store holds a contest to attract shoppers. Once an hour someone in the store is chosen at random to play the Music Game. Using the winning amounts given in the book what is the average dollar amount of music the store will give away?

wrong: 15-25

x 2 5 6 8 10y 5 27 35 65 101 Find a POWER model to describe this data.

y=1.35x^1.86

An analysis of the relationship between the number of telephones in a household (x) and the annual family income (y) revealed the following statistics: xbar = 3.8 ybar = 65,000 n = 26 Sx = 1.2 Sy = 15,500 r = 0.65 Determine the least-squares regression line.Give your answer (rounded to integers) in the form:[predicted annual family income] =__________ + ____________ (# telephones in household)

yhat = a + bx where b is slope and = (r(Sy/Sx)) = 8396 substituting xbar and ybar as a known point on the line we solve for a and get approx. 33096 [annual family income] = 33096 + 8396*[#telephones in household]

Ch 11_8After simulating the spread of a disease, a researcher wrote, "24% of the people contracted the disease." What should the correct conclusion be? (Give this some thought before responding)

24% of the people may contract the disease.

A school board study found a moderately strong negative association between the number of hours high shcool seniors worked at part-time jobs after school hours and the students' grade point averages.Hoping to improve student performace, the school board passed a resolution urging parents to limit the number of hours students be allowed to work. Discuss the school board's reasoning.DO YOU AGREE OR NOT?

Association does not mean causal. Only experiments can prove causation.

Ch10_23dDo you think that the model will produce accurate predictions about the gas mileage people may get in daily driving? Explain completely.

I do no think so. This is because people do not drive at a consistent speed every single day. People go through differnt regions which can have different speeds or they may have consequential need which cause them to speed, therefore it is not reasonable to assume that these people will drive at the same speed every day and use the same gas mileage.

Consider the scatterplot of midterm and final exam scores for a class of 15 students. Which of the following are true statements? Read each statement and decide on its validity before selecting your answer.I. The same number of students scored 100 on the midterm exam as scored 100 on the final exam.II. Students who scored higher on the midterm exam tended to score higher on the final exam.III. The scatterplot shows a moderate negative correlation between midterm and final exam scores.

I and III

Which of the following are true statements? I. The standard deviation is the square root of the variance. II. The standard deviation is zero only when all values are the same. III. The standard deviation is strongly affected by outliers

I, II, and III

With regard to regression, which of the following statements about outliers are true?I. Outliers have large residuals.II. A point may not be an INFLUENTIALoutlier even though its x-value is an outlier in the x-variable and its y-value is an outlier in the y-variable.III. Removal of an outlier sharply affects the regression line.

I, II, and III

Chapter 2 Exercises #16 Which of these are categorical variables? I. size II. # of years in existence III. varieties of grapes grown

III

It would be best to answer the question a nd then go on and supply the logic that produced that result.Is it easier for the best National Basketball Association (NBA) players to get a rebound or an assist? The data was taken during the 1994-1995 season.The top 20 rebounding leaders averaged the following numbers of rebounds per game:16.8 (Rodman), 12.6, 11.4, 11.1, 11.0, 10.9, 10.9, 10.9, 10.8, 10.8, 10.6, 10.6, 10.6, 10.4, 10.3, 9.9, 9.7, 9.7, 9.6, and 9.4 The top 20 assist leaders averaged the following number of assists per game:12.3 (Stockton), 9.4, 9.3, 8.8, 8.7, 8.3, 8.2, 7.9, 7.7, 7.7, 7.6, 7.5, 7.3, 7.2, 7.1, 6.9, 6.4, 6.2, 6.1, and 5.7*Compare these data using a pair of distributions. It is not necessary to show your graph.*Comment on shape and outliers.You must comment enough so that your response can be followed WITHOUT a picture!Make sure you answer the original question...which is easier...rebound or assist???

It is easier to rebound than it is to assist. The data for rebound has a higher mean of 10.9, as opposed to assist which has a mean of 7.8. The spread of the data for rebound is larger, with a range of 7.4, whereas assit has a range of 6.6. This only shows that assists happen less frequently, with only one high outlier being 12.3. Rebound also has a smaller IQR, of .85, which shows that it is more likely to score more rebounds consistantly; whereas, assist has an IQR of 1.5. Rebound has a small IQR which is reflected in its 2 outliers, 16.8 and 12.6. However, even without these, rebounds are still more likely to occur in a game (all based on average for both).

A study was conducted on the weights of three different species of fish found in a lake in Finland. These three fish (bream, perch and roach) are commercial fish. Their weights are displayed in the boxplots above. Which of the following statements comparing these boxplots is NOT correct?

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