AP Statistics Quiz - Chapter 3 Name

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In order to plan transportation and parking needs at aprivate high school, administrators asked students howthey get to school. Some rode a school bus, some rode inwith parents or friends, and others used "personal"transportation - bikes, skateboards, or just walked. Thetable summarizes the responses from boys and girls.

1. Identify the variables and tell whether each is categorical or quantitative.

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Male Female TotalBus 30 34 64Ride 37 45 82Personal 19 23 42Total 86 102 188

3. Find each percent.a) What percent of the students are girls who ride the bus?b) What percent of the girls ride the bus?c) What percent of the bus riders are girls?

4. What is the marginal distribution of gender?

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NameAP Statistics Quiz - Chapter 51. The five-number summary for the weights (in pounds) of fish caught in a bass

tournament is 2.3 - 2.8 - 3.0 - 3.3 - 4.5.

a) Would you expect the mean weight of all fish caught to be higher or lower thant h e m e d i a n ? E x p l a i n . 0 , i , i ir m 4 i " V £ i W f • * * - M A C K . * . w . l |

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b) You caught 3 bass weighing 2.3 pounds, 3.9 pounds, and 4.2 pounds. Were any of• your fish outliers? Explain.

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2. The boxplots show prices of used cars (in thousands ofdollars) advertised for sale at three different car dealers.a) Which dealer offers the cheapest car offered, and at

what price?

b) Which dealer has the lowest median price, and howmuch is it?

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d) Which dealer's prices have the smallest IQR, andw h a t i s i t ? ,

( g ^ - » \ H K - \ \ k " % g f * >e) Which dealer generally sells cars cheapest? Explain.

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AP Statistics Quiz - Chapter 6 Name

City planners wanted to know how many people lived in atypical housing unit so they compiled data from hundreds offorms that had been submitted in various city offices. Summarystatistics are shown in the table.a) Notice that the minimum occupancy and the first quartile

are the same. Explain how this can be.

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b) The city classifies residences housing 4 or more people as "high occupancy".Would you consider 4 occupants to be unusually high? Explain.

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c) The city bases their garbage disposal fee on the occupancy level of the home orapartment. The annual fee is $40 plus $5 per person, so a single occupant pays $45and the homes with 10 people pay $40 +10($5) = $90 a year. What is the medianfee paid? And the IQR?

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d) What are the mean and standard deviation of the garbage disposal fees?

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2. Owners of a minor league baseball team believe that a Normal model is useful inprojecting the number of fans who will attend home games. They use a mean of 8500fans and a standard deviation of 1500 fans. Draw and clearly label this model.

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3. Although most of us buy milk by the quart or gallon, farmers measure dailyproduction in pounds. Guernsey cows average 39 pounds of milk a day with astandard deviation of 8 pounds. For Jerseys the mean daily production is 43 poundswith a standard deviation of 5 pounds. When being shown at a state fair a championGuernsey and a champion Jersey each gave 54 pounds of milk. Which cow's milkproduction was more remarkable? Explain. ™,__

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4. A company's manufacturing process uses^OTTgalTonTof̂ 'water at a time. A"scrubbing" machine then removes most of a chemical pollutant before pumping thewater into a nearby lake. Legally the treated water should contain no more than 80parts per million of the chemical, but the machine isn't perfect and it is costly tooperate. Since there's a fine if the discharged water exceeds the legal maximum, thecompany sets the machine to attain an average of 75 ppm for the batches of watertreated. They believe the machine's output can be described by a Normal model withs t a n d a r d d e v i a t i o n 4 . 2 p p m . ( s h o w w o r k )a) What percent of the batches of water discharged exceed the 80ppm standard?

b) The company's lawyers insist that they not have more than 2% of the water overthe limit. To what mean value should the company set the scrubbing machine?Assume the standard deviation does not change.

c) Because achieving a mean that low would raise the costs too much, they decide toleave the mean set at 75 ppm and try to reduce the standard deviation to achievethe "only 2% over" goal. Find the new SD needed.

f d) Explain what achieving a smaller standard deviation means in this context.

NameAP Stats Test - Unit IJt_ 1. We collect these data from 50 male students. Which variable is categorical?

A) eye color B) head circumference C) hours of homework last weekD) number of cigarettes smoked daily E) number of TV sets at home

12.2. Which of those variables is most likely to be bimodal?D 3. Which of those variables is most likely to follow a Normal model?12_ 4. The mean number of hours worked for the 30 males was 6, and for the 20 femaleswas 9. The overall mean number of hours worked ... b Lo**) + ^ Lo^J s 7^2A) is 6.5 B) is 7.2 C) is 7.5 D) is none of these. E) cannot be determined.\J_ 5. We might choose to display data with a stemplot rather than a boxplot because astemplot... I. reveals the shape of the distribution.

II. is better for large <flata sets.III. displays the actual data.

A) I only B) II only C) III only D) I and III only E) I, II, and III' ' 6. Which is true of the data whose distribution is shown?

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.A) I only B) II only C) I and II D) II and III E) I, II, and III

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A) 5. B) 8. C) 12. D) 18. E) 20.tiL 8. Suppose that a Normal model describes theacidity (pH) of rainwater, and that water testedafter last week's storm had a z-score of 1.8. This means that the acidity of that rain ..A) had a pH of 1.8. B) varied with a standard deviation of 1.C) had a pH 1.8 higher than average rainfall.D) 8had a pH 1.8 times that of average rainwater.E) had a pH 1.8 standard deviations higher than that of average rainwater.

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9. The ages of people attending the openingshow of a new movie are summarized in theogive shown. Estimate the IQR of the ages.A) 5 B)13 C)21 D)30 E) 37Lr 10. Environmental researchers have collectedrain acidity data for several decades. They wantto see if there is any evidence that attempts toreduce industrial pollution have produced atrend toward less acidic rainfall. They shoulddisplay their data in a(n)...A) contingency table B) bar graph

C) boxplot D) histogram E) timeplot

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11. Shopping One day a store tracked theway shoppers paid for their purchases. Their

/^ data are summarized in the table.a) What percent of the men paid cash?

Cash Check Charge TotalMale 18 10 12 40Female 18 12 30 60Total 36 22 42 100

C&£ U • 5 0% ctacK \ lo X cWjC \ ^D^jb) What is the conditional relative frequencydistribution of payment method for women?

c) If you wanted to show the association between gender and method of paymentvisually, what kind of graph would you make? (Just name it.) O |

d) Is there evidence of an association between gender and method of payment? Explainb r i e fl y . f o A : f ^ k , ^ / > 0 C W k \ 2 & C k ^ r , ^

v<12. Car Repairs An automobile service shop reported the summarystatistics shown for repair bills (in $) for their customers last month,a) Were any of the bills outliers? Show how you made your decision.

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Min 27Q i 88Median 132Q3 308Max 1442Mean 284StDev 140

b) After checking out a problem with your car the service manager gives you an estimateof "only $90". Is he right to imply that your bill will be unusually low? Explain briefly.

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13. Working Overseas You learn that your company is sending you and several otheremployees to staff a new office in China. While there everyone will earn the equivalent oftheir current salary, converted to Chinese currency at the rate of 8 yuans per dollar. Inaddition, everyone will earn a weekly foreign living allowance of 200 yuans. For example,since you are earning $1000 per week, your weekly salary in China will be 1000 x 8 + 200= 8200 yuans.a) Shown are some summary statistics

describing the current salaries of thisgroup being sent overseas. Fill in thetable to show what these statistics willbe for the salaries you all will earn whilein China.

b) Among this group of employees goingto China, your US salary has a z-score of +1.20. What will your new z-score be, basedon everyone's China salary?

Statistic In the US In ChinaMinimum salary $400 l l o oStandard deviation $250 %oooMedian $750 (olrOOIQR $300 i-HoO

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14. Copiers A manufacturer claims that lifespans for their copy machines (in months)c a n b e d e s c r i b e d b y a N o r m a l m o d e l N ( 4 2 , 7 ) . [ S H O W W O R K ]

a) Draw and clearly label the model.

b) A company with a several large office buildings buys 200 of these copiers. Thesalesman tells the boss "190 (95%) of your new copiers will last between 2g> and5(e months". Comment on this claim.

c) What is the 3rd quartile of copier lifespans?

d) What percent of the copiers are expected to fail before 36 months?

1-e) The manufacturer wants to reduce the 36-month failure rate to only 10%.

Assuming the mean lifespan will stay the same, what standard deviation mustthey achieve?

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f) Briefly explain what that change in standard deviation means in this context.

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g) A competing manufacturer says that not only will 90% of their copiers last at least36 months, 65% will last at least 42 months. What Normal model parameters is thatm a n u f a c t u r e r c l a i m i n g ? [ S h o w w o r k o n t h e b a c k . ] ,

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AP Stats Quiz - Chapter 7 Name

_ 1. After conducting a marketing study to see what consumers thought about a new( tinted contact lens they were developing, an eyewear company reported, "Consumersatisfaction is strongly correlated with eye color." Comment on this observation.

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2. On the axes below, sketch a scatterplot described:a) a strong negative b) a strong association,

a s s o c i a t i o n b u t r i s n e a r 0 c) a weak butpositive association

3. A school board study found a moderately strong negative association between thenumber of hours high school seniors worked at part-time jobs after school hours andthe students' grade point averages,a) Explain in this context what "negative association" means.

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b) Hoping to improve student performance, the school board passed a resolutionurging parents to limit the number of hours students be allowed to work. Discussthe school board's reasoning.

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4. Researchers investigating theassociation between the size andstrength of muscles measured theforearm circumference (in inches)of 20 teenage boys. Then theymeasured the strength of the boys'grips (in pounds). Their data areplotted at the right.

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a) Write a few sentences describing the association.

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b) Estimate the correlation. r= 0-4c) If the point in the lower right corner (at about 14" and 38#) were removed, how

would the correlation become stronger, weaker, or remain about the same?

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d) If the point in the upper right corner (at about 15" and 75#) were removed, wouldthe correlation become stronger, weaker, or remain about the same?

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A P S t a t Te s t - L i n e a r R e g r e s s i o n N a m eC^l. Child development researchers studying growth patterns of children collect data on theheights of fathers and sons. The correlation between the fathers' heights and the heights of their16 year-old sons is most likely to be ...A) near -1.0 B) near 0 C) near +0.7 D) exactly +1.0 E) somewhat greater than 1.0K 2. The aujjefinsurance industry crashed some test vehicles into a cement barrier at speeds of 5to 25 mph to/investigate the^amount of carnage to the c^rs. They found a correlation of r = 0.60between $jfeed (MPH) an^amage ($)/lf the speed at \vhich a car hit the barrier is 1.5 standard _ / f \\deviations above the mean speed, vf4 expect the damage to be..,?.. ^the mean damage. I. ^> v ^»QJA) equal to B) 0.36 SD above ' C) 0.60 SD above D) 0.90 SD above E) 1.5 SD aboveC^ 3. Which scatterplot shows a strong association between two variables even though the jcorrelation is probably near zero?

• • i f * flA ) [ • B ) l C ) l D ) l H E )£14. The correlation between X and Y is r = 0.35. If we double each X value, decrease each Y by0.20, and interchange the variables (put X on the Y-axis and vice versa), the new correlation

A) is 0.35 B) is 0.50 C) is 0.70 . D) is 0.90 E) cannot be determined.Sr^5. A consumer group collected information on standard color TVs (no HDTV or large screensets). They created a linear model to estimate the cost of a TV (in $) based on the screen size (ininches). Which is the most likely value of the slope of the line of best fit?q A ) 0 . 2 5 B ) 2 . 5 Q 2 5 . 0 D ) 2 5 0 . 0 E ) 2 5 0 0 . 0

/^N O 6. The correlation between a family's weekly income and the amount they spend on restaurantmeals is found to be r = 0.30. Which must be true?

I. Families tend to spend about 30% of their incomes in restaurants.II. In general, the higher the income, the more the family spends in restaurants.Ill The line of best fit passes through 30% of the (income, restaurant$) data points.

A ) I o n l y B ) I I o n l y C ) I I I o n l y D ) I I a n d I I I o n l y E ) I , I I , a n d I I I\J_ 7. A medical researcher finds that the more overweight a person is, the higher his pulse ratetends to be. In fact, the model suggests that 12-pound differences in weight are associated withdifferences in pulse rate of 4 beats per minute. Which is true?

I. The correlation between pulse rate and weight is 0.33II. If you lose 6 pounds, your pulse rate will slow down 2 beats per minute.III. A positive residual means a person's pulse rate is higher than the model predicts.

. A) none B) I on ly C) I I on ly D) I I I on ly E) I I and I I I on lyd 8. Education ^earclyfonsisterrtjy shows that stents fropf wealthier family tend p6 have/higher SAYsc^es. TlWslope of/fhe line t$at presets SATpore fromfamily indme is 6^5 ppiMsper $1000f any the co/elationJfetween me variables is 0M. Then tm slope/f the ljife thp/predicWfamily income from SAT score (m $1000g>er poin^... /y y A ) i s 0 .037 B ) i s 0 .16 C ) i s 3 .00 D ) i s 6 .25 E ) i s c13 .02 .

SJl9. A regression analysis of company profits and the amount of money the company spent onadvertising found r2 = 0.72. Which of these is true?

I. This model can correctly predict the profit for 72% of companies.

^^ II. On average, about 72% of a company's profit results from advertising.( III. On average, companies spend about 72% of their profits on advertising.

A) none B) I only C) II only D) II I only E) I and III8-13

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10. A least squares line of regression has been fitted to a scatterplot; themodel's residuals plot is shown. Which is true?

A) The linear model is appropriate.B) The linear model is poor because some residuals are large.C) The linear model is poor because the correlation is near 0.D) A curved model would be better.E) None of the above.

11. Earning Power A college's job placement office collected data about students' GPAs and thesalaries they earned in their first jobs after graduation. The mean GPA was 2.9 with a standarddeviation of 0.4. Starting salaries had a mean of $47200 with a SD of $8500. The correlationbetween the two variables was r = 0.72. The association appeared to be linear in the scatterplot.

(Show work)a) Write ar/equat^r/of the npdel the/can predict sala^f basecj/on GPj

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b) Do you think these predictions will be reliable? Explain.

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c) Yourfcrother just graduated froir/that college witfi a GPA of 3.pb. He tells /ou tha^ basedon tjftis model the residual for hjfe pay is -$1880. j^hat salary i/he earning

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12. Assembly Line Your new job at Panasony is to do the final assembly ofcamcorders. As you learn how, you get faster. The company tells you that youwill qualify for a raise if after 13 weeks your assembly time averages under 20minutes. The data shows your average assembly time during each of your first10 weeks.

a) Which is the explanatory variable? W<*Ks W^fedb) What is the correlation between these variables? V~- "~ O^-fc) You want to predict whether or not you will qualify for that raise.

Would it be appropriate to use a linear model? Explain.

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13. Associations For each pair of variables, indicate what association you expect: positive(+),negative(-), curved(C), or none(N).

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power level setting of a microwavenumber of days it rained in a month(during the summer)number of hours a person has been uppast a normal bedtimenumber of hockey games played inMinnesota during a weeklength of a student's hair

number of minutes it takes to boil waternumber of times you mowed your lawn thatmonthnumber of minutes it takes the person to do acrossword puzzlesales of suntan lotion in Minnesota during thatweeknumber of credits the student earned last year

14. Music and Grades (True Story) A couple of years ago a local newspaper published researchresults claiming a positive association between the number of years high school children hadtaken instrumental music lessons and their performances in school (GPA).

a) What does "positive association" mean in this context?

b) A group of parents then went to the School Board demanding more funding for musicprograms as a way to improve student chances for academic success in high school. As astatistician, do you agree or disagree with their reasoning? Explain briefly.

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15. Gas Mileage Again In the DataDesklab last week you analyzed theassociation between a car's fueleconomy and its weight. Anotherimportant factor in the amount ofgasoline a car uses is the size of theengine. Called "displacement", enginesize measures the volume of thecylinders in cubic inches. The regressionanalysis is shown.

a) How many cars were includedin this analysis?

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D e p e n d e n t v a r i a b l e i s : m p g89 total cases of which 0 are missingR squared = 60.9% R squared (adjusted) = 60.0%s = 3.056 with 89 - 2 = 87 degrees of freedom

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9J&>.What is the correlation between engine size and fuel economy?A car you are thinking of buying is available with two different size engines, 190 cubicinches or 240 cubic inches. How much difference might this make in your gas mileage?(Show work)

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16. Crawling Researchers at the University of Denver Infant Study Center investigated whetherbabies take longer to learn to crawl in cold months (when they are often bundled in clothes thatrestrict their movement) than in warmer months. The study sought an association betweenbabies' first crawling age (in weeks) and the average temperature during the month they first tryto crawl (about 6 months after birth). Between 1988 and 1991 parents reported the birth monthand age at which their child was first able to creep or crawl a distance of four feet in one minute.Data were collected on 208 boys and 206 girls. The graph below plots average crawling ages (inweeks) against the mean temperatures when the babies were 6 months old. The researchers founda correlation of r = -0.70 and their line of best fit was

AvAge = 36 - 0.08 AvTemp.34.0

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a) Draw the line of best fit on the graph. (Show your method clearly.)

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b) Describe the association in context.W a

c) Explain (in context) what the slope of the line means.

. d) Explain (in context) what the y-intercept of the line means.

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e) Explain (in context) what r~means.

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f) In this context, what does a negative residual indicate?

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AP Statistics Quiz - Chapter 11 NameAs a 4-H project, Billy is raising chickens. He feeds and waters them every day, and

^ collects the eggs every other day, selling them to people in the neighborhood. He hasfound that each hen's nest will contain from 0 to 2 eggs. Based on past experience heestimates that there will be no eggs in 10% of the nests, one egg in 30% of the nests, and 2eggs in the other 60%. Conduct a simulation to estimate how many nests Billy will haveto visit to collect a dozen eggs.1. Describe how you will use a random number table to conduct this simulation.

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f*^ 2. Show three trials by clearly labeling the random number table given below. Specifythe outcome for each trial.

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3. State your conclusion.

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A P S t a t i s t i c s T e s t - C o l l e c t i n g D a t a N a m e/** 1. If we wish to compare the average PS AT scores of boys and girls taking AP Statistics atthis high school, which would be the best way to gather these data?A) census B) SRS C) stratified sample D) observational study E) experiment¥ 2. A factory has 20 assembly lines producing a popular toy. To inspect a representative

sample of 100 toys, quality control staff randomly selected 5 toys from each line's output. Wasthis a simple random sample?

A) Yes, because the toys were selected at random.B) Yes, because each toy produced had an equal chance to be selected.C) Yes, because a stratified sample is a type of simple random sample.D) No, because not all combinations of 100 toys could have been chosen.

/«. E) No, because toys do not come off the assembly line at random.r 3. Which is true about sampling error?

I. An attempt to take a census will always result in less error than using a sample.II. Sampling error is usually reduced when the sample size is larger.III. Sampling error is the result of random variations and is always present.

r A ) I o n l y B ) I I o n l y C ) I I I o n l y D ) I I a n d I I I E ) a l l t h r e e^ 4. The owner of a car dealership planned to develop strategies to increase sales. He hoped tolearn the reasons why many people who visit his car lot do not eventually buy a car from him.For one month he asked his sales staff to keep a list of the names and addresses of everyone whocame in to test drive a car. At the end of the month he sent surveys to the people who did not buythe car, asking them why. About one third of them returned the survey, with 44% of thoseindicating that they found a lower price elsewhere. Which is true?

I. The population of interest is all potential car buyers.I I . T h i s s u r v e y d e s i g n s u f f e r e d f r o m n o n - r e s p o n s e b i a s . " ^ ^III. Because it comes from a sample 44% is a parameter, not a statistic.

A) I only B) II only C) I and II only D) II and III only E) I, II, and III^-^ 5. Does regular exercise decrease the risk of cancer? A researcher finds 200 women over 50who exercise regularly, pairs each with a woman who has a similar medical history but does notexercise, then follows the subjects for 10 years to see which group develops more cancer. This is a

A) survey B) re t rospect ive s tudy C) prospect ive s tudyD) randomized experiment E) matched experiment

*^" 6. Which is important in designing a good experiment?I. Randomization in assigning subjects to treatments.II. Control of potentially confounding variables.III. Replication of the experiment on a sufficient number of subjects.

A) I only B) I and II C) I and III D) II and III E) all threeL^ 7. Can watching a movie temporarily raise your pulse rate? Researchers have 50 volunteerscheck their pulse rates. Then they watch an action film, after which they take check their pulserates once more. Which aspect of experimentation is present in this research?A) a placebo B) blinding C) randomization D) a control group E) none of these£..8. In an experiment the primary purpose of blocking is to reduceA) bias. B) confounding. C) randomness. D) undercoverage. E) variat ion.

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JZ 9. To check the effect of cold temperatures on the battery's ability to start a car researcherspurchased a battery from Sears and one from NAPA. They disabled a car so it would not start,put the car in a warm garage, and installed the Sears battery. They tried to start the carrepeatedly, keeping track of the total time that elapsed before the battery could no longer turn theengine over. Then they moved the car outdoors where the temperature was below zero. After thecar had chilled there for several hours the researchers installed the NAPA battery and repeatedthe test. Is this a good experimental design?

A) YesB) No, because the car and the batteries were not chosen at random.C) No, because they should have tested other brands of batteries, too.D) No, because they should have tested more temperatures.

^ E) No, because temperature is confounded by brand.^10. Twenty dogs and 20 cats were subjects in an experiment to test the effectiveness of a newflea control chemical. Ten of the dogs and 10 of the cats were randomly assigned to anexperimental group that wore a collar containing the chemical, while the others wore a similarcollar without the chemical. After 30 days veterinarians were asked to inspect the animals forfleas and evidence of flea bites. This experiment is...

A) completely randomized with one factor: the type of collarB) completely randomized with one factor: the species of animalC) randomized block, blocked by speciesD) randomized block, blocked by type of collarE) completely randomized with two factors

11. ^ A member of the City Council has proposed a resolution opposing construction of a newstate prison there. The council members decide they want to assess public opinion before theyvote on this resolution. Below are some of the methods that are proposed to sample local

^ residents to determine the level of public support for the resolution. Match each with one of the( listed sampling techniques._J2_ a) Place an announcement in the newspaper asking people to call their council

representatives to register their opinions. Council members will tally the calls they receive.Jz. b) Have each council member survey 50 friends, neighbors, or co

workers._j±L c) Have the Board of Elections assign each voter a number, then select

400 of them using a random number table._i_ d) Go to a downtown street corner, a grocery store, and a shopping

mall; interview 100 typical shoppers at each location.A_ e) Randomly pick 50 voters from each election district._X f) Call every 500th person in the phone book.Jj_ g) Randomly pick several city blocks, then randomly pick 10 residents

from each block.JL h) Randomly select several city blocks; interview all the adults living on each block.12. The City Council decides to conduct a telephone poll. Pollsters ask a carefully chosenrandom sample of adults this question: "Do you favor the construction of a new prison to deal with thehigh level of violent crime in our State?" In what way might the proportion of "Yes" answers fail toaccurately reflect true public opinion? Explain briefly. What kind of bias is this?

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13. The Mars candy company starts a marketing campaign that puts a plastic game piece ineach bag of M&Ms. 25% of the pieces show the letter "M", 10% show the symbol "&", and the restjust say 'Try again'7. When you collect a set of three symbols "M", "&", and "M" you can turnthem in for a free bag of candy. About how many bags will a consumer have to buy to get a freeone? Use a simulation to find out.

a) Explain how you will use the random numbers listed below to conduct your simulation.M

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b) Carefully label your simulation for 2 trials.Trial # The run Outcome

1 6 9 0 7 4 9 1 9 7 6 3 3 5 8 4 9 4 1 3 8 8 7 6 3 7T M T A l T f lo

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c) State your conclusion.av<9 J X ) < \ g j " n ^ o y d ~

14. Leather furniture used in public places can fade, crack, anddeteriorate rapidly. An airport manager wants to see if a leatherpreservative spray can make the furniture look good longer. Hebuys eight new leather chairs and places them in the waiting area,four near the south-facing windows and the other four set backfrom the windows as shown. He assigned the chairs randomly tothese spots.

a) Use the random numbers given to decide which chairs tospray. Explain your method clearly.

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15. Marketing researchers wonder if the color and type of a candy's packaging may influencesales of the candy. They manufacture test packages for chocolate mints in three colors (white,green, and silver) and three types (box, bag, and roll). Suspecting that sales may depend on a

^ combination of package color and type, the researchers prepare nine different packages, thenmarket them for several weeks in convenience stores in various locations. In this experimenta) what are the experimental units? pA^^^HL-3>b) how many fac to rs a re there? *c) how many treatments are there? id) what is the response var iab le? Saf^S

16. A recent study evaluated elementary age children for aggressiveness. This study foundthat the children who played video games were more likely to engage in aggressive or violentplay at school. The researchers said the difference was statistically significant.

a) Br iefly expla in what "stat is t ica l ly s ignificant" means in th is context . ,

b) The news media reported that this study proved that playing computer games causeschildren to be aggressive or violent. Briefly explain why this conclusion is not justified.

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c) But perhaps it is true. We wonder if playing computer games can lead to aggressive or( violent behavior in elementary school children. We find 50 young children whose families

volunteer to participate in our research. Design an appropriate experiment. (You need notexplain how to randomize.)

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A sporting goods store announces a " Wheel of Savings'7sale. Customers select the merchandise they want topurchase, then at the cash register they spin a wheel todetermine the size of the discount they will receive. Thewheel is divided into 12 regions, like a clock. Six of thoseregions are red, and award a 10% discount. The three whiteregions award a 20% discount and two blue regions a 40%discount. The remaining region is gold, and a customerwhose lucky spin lands there gets a 100% discount - them e r c h a n d i s e f r e e ! [ S h o w W o r k ]

1. What is the probability that a customer gets at least a 40% discount?

|Z- = €?."2-S i i r2. What is the probability that two customers in a row get only 10% discounts?

( o k ^7L ' ix = O,^ c?.ai~3. What is the probability that three consecutive customers all get 20% discounts?

CD - o> ol e.Qll,4. What is the probability that none of the first four customers gets a discount over 20%?

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5. What is the probability that the first gold winner (100%) is the fifth customer in line?

6. What is the probability that there is at least one gold winner among the first sixcustomers?

H-\4I- pU*$>\±) = \-(.fi) 0.H0+7. As you wait your turn in line there are three gold winners in a row. A lively

discussion ensues between the next two customers. One thinks that streak about killsher chances of winning free merchandise, as the wheel wont come up gold again for avery long time. The other says that the wheel is clearly on a hot streak, so they arelucky to be next in line. Comment on their opinions.

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A P S t a t i s t i c s Q u i z - C h a p t e r 2 5 N a m e1. A survey of local car dealers revealed that 64% of all cars sold last month had CD

players, 28% had alarm systems, and 22% had both CD players and alarm systems,a) What is the probability one of these cars selected at random had neither a CD

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system?

c) What is the probability a car with an alarm system had a CD player?

d) Are having a CD player and an alarm system disjoint events? Explain.

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2. All airline passengers must pass through securityscreenings, but some are subjected to additionalsearches as well. Some travelers who carry laptopswonder if that makes them more likely to be searched.Data for 420 passengers aboard a cross-country flightare summarized in the table shown. Does it appear that being subjected to anadditional search is independent of carrying a laptop computer? Explain.

Searched?Yes No Total

Laptop 30 42 72No laptop 145 203 348

Total 175 245 420

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For purposes of making on-campus housing assignments, a college classifies itsstudents as Priority A (seniors), Priority B (juniors), and Priority C (freshmen andsophomores). Of the students who choose to live on campus, 10% are seniors, 20% arejuniors, and the rest are underclassmen. The most desirable dorm is the newlyconstructed Gold dorm, and 60% of the seniors elect to live there. 15% of the juniorsalso live there, along with only 5% of the freshmen and sophomores. What is theprobability that a randomly selected resident of the Gold dorm is a>eniar?^ow yourwork clearly on the back of this page.

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A P S t a t i s t i c s Q u i z - C h a p t e r 1 6 N a m eA small business just leased a new computer and color laser printer for three years. Theservice contract for the computer offers unlimited repairs for a fee of $100 a year plus a$25 service charge for each repair needed. The company's research suggested that duringa given year 86% of these computers needed no repairs, 9% needed to be repaired once,4% twice, 1% three times, and none required more than three repairs.1. Find the expected number of repairs this kind of computer is expected to need each

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the standard deviation of the number of repairs each year , ~ \2. Find the standard deviation of the number of repairs each year.

3. What are the mean and standard deviation of the company's annual expense for mes e r v i c e c o n t r a c t ? ^ ^

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r - Ig?. i> "^ (T, /$r£$4. How many times should the company expect to have to get this computer repaired

over the three-year term of the lease?

5. What is the standard deviation of the number of repairs that may be required duringthe three-year lease period? On what assumption does your calculation rest? Do youthink this assumption is reasonable? Explain.

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6. The service contract for the printer estimates a mean annual cost of $120 withstandard deviation of $30. What is the expected value and standard deviation of thetotal cost for the service contracts on computer and printer?

x+y - ios~4 no * Aw- ^ ^7. Which service contract should the company expect to cost more each year? How much

more? With what standard deviation?

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