AP Stats Final
opinion polling organizations contact their respondents by sampling random telephone numbers. assume that interviewers can now reach about 71% of U.S. households, while the percentage of those contacted who agree to cooperate with the survey is 31%. each household, it can be safely assumed, is independent of the others. what is the probability of failing to contact a household or of contacting the household but not getting them to agree to the interview?
0.78
at a sporting event, cheerleaders will throw 50 bundled t-shirts into the crowd. the t-shirt sizes consist of 10 small, 15 medium, and the remainder either large or extra large. suppose Ana catches a t-shirt. what is the probability that she will catch a t-shirt that is not a size small?
0.80
teacher has 78 students, 35 in band, 32 in sports, one will be selected at random. are B and S mutually exclusive?
no, because P(B[union symbol]S) = 5/78
baggage items, time required to delver items. a scatterplot between the two variables indicated a strong, positive, linear association between the variables. which of the following statements is a correct interpretation of the word "strong" in the description of the association?
the actual time required to deliver all the items to the baggage claim area based on the number of items unloaded will be very close to the time predicted by a least-squares model.
one student from the school will be selected at random. what is the probability that the student is in the age-group 6 to 8 given that the student responded joy?
28/89
which of the following can be used to show a cause-and-effect relationship between two variables?
a controlled experiment
the least squares regression line produced from a random sample is milk (hat) = 40.8-1.1(age). based on the model, what is the difference in predicted amounts of milk produced between a cow of 5 years, and a cow of 10 years?
a cow of 5 years is predicted to produce 5.5 more gallons per week
in the reporters article it was stated that a random sample of the students showed that 89% of the school;s population was happy with the new menu. which of the following statements is true?
because students self-selected whether to eat in the cafeteria, the sampling method might be biased and the sample might not be representative of all students in the school
TEST 3: why does the correlation value of 0.94 not necessarily indicate that a linear model is the most appropriate model for the relationship between length of an aspen leaf and its surface area?
even with a correlation of 0.94, it is possible that the relationship could still be better represented by a nonlinear model
210 were surveyed. 70 adults, 140 children. 150 indicate cone as preferred method of eating ice cream. there was no association between age and preferred method of eating. which of the following tables shows the distribution of the responses?
table C (50 adults-cone; 100 children-cone; 20 adults-cup; 40 children-cup)
magazine, sat scores, etc. which of the following explains why, in this situation, the median is a more accurate indicator of the SAT score of the average student than the mean is?
the mean is affected by the skewness, whereas the median is not
list the sample space and tell whether the outcomes are equally likely, a family has two children; record the number of girls
{0, 1, 2} not equally likely
the histogram shows the distribution of height, in inches (in), of 100 adult men. based on the following histogram, which of the following is closest to the interquartile range, in inches (in), of the distribution?
5
a fair coin has come up "heads" 10 times in a row. the probability that the coin will come up heads on the next flip is
50%
if the owners beliefs are correct, which of the following statements must be true concerning event A and event B?
event A and event B are not mutually exclusive and are independent
some descriptive statistics for a set of test scores are shown below. for this test, a certain student has a standardized score of z= -1.2. what score did this student receive on the test?
779.42
the sale bin in a clothing store contains an assortment of t-shirts in diff sizes. there are 9 small, 7 medium, and 4 large. alan is looking for a large shirt. he starts grabbing shirts one at a time and checking the size. after he checks, he leaves it outside the bin. what is the probability that the first large shirt he finds is the third one he checks?
0.140
based on the meteorologists estimates, approximately what is the probability that a future tropical storm will originate in the pacific ocean and be classified as major?
0.170
at a california school, 22% of students speak spanish, 5% speak french, and 3% speak both. what is the probability that a student chosen at random speaks spanish but not french?
0.19
if one flight is selected at random from the airport in january, what is the probability that the flight selected will have at least one of the two types of delays?
0.335
in a parking lot with 200 cars, 50 are white, 30 are red, 20 are silver. one car will be selected at random from the parking lot. if each car in the parking lot has only one color, which of the following cannot be the probability that the selected car will be green?
0.6
prior to beginning the speed check, the officer estimates that 40% of the motorists will be driving more than 5 miles per hour over the speed limit. assuming that the police officers estimate is correct, what is the probability that among 4 randomly selected motorists, he officer will find at least 1 motorist driving more than 5 miles over the speed limit?
0.8704 (1-[.6]^4)
a large store has a customer service department where customers can go to ask for help. according to records, approx. 1/4 of customers who go to service department ask for help. assume the reason each customer goes to the service department is independent from customer to customer. based on the approximation, what is the prob. that at least 1 of the next 4 customers who go to service department will ask for help?
1-(3/4)^4
8-ounce can is approximately normally distributed with mean 33 mg. a randomly selected can 35 mg is 1.2 standard deviations above the mean. approx. what % of 8-ounce cans have a caffeine content greater than 35 mg?
12%
TEST 2: scientists estimate that the distributions of the life span of the galapagos islands giant tortoise is approximately normal with mean 100 years and standard deviation 15 years. based on estimate, which of the following is closest to the age of a galapagos island tortoise in the 90th percentile of the distribution.
120 years (z score= 1.28; x-mean/standard deviation= z score)
90% of the people who have a particular disease will have a positive result on a given diagnostic test. 90% of people who do not have the disease will have a negative result on this test. if 5% of a certain population has the disease, what percent of that population would test positive for the disease?
14% (i think it is 4.5% bc of the way its worded but ask ms.kopatic on the day of the final)
puzzle, small in 75, large in 140, mean for small 60 minutes with SD of 15, mean for large 180 minutes with SD of 40. approx. what percentage of the participants had finishing times greater than shalise's for each puzzle?
16% on the small puzzle and 84% on the large puzzle
male grizzly- mean 500 lbs, SD 50 lbs; female grizzly- mean 300 lbs, SD 40 lbs. approx. what would be the weight of a female grizzly with the same standardized z-score as a male grizzly bear with a weight of 530 pounds?
324 pounds
one senior from the high schools will be selected at random. what is the probability that the senior selected will not be from high school B given that the senior responded with a choice other than college?
396/538
candy, weight, normally distributed with mean 720 mg, etc. if the manager's belief is correct, which of the following intervals of weights will contain the largest proportion of the candies in the distribution of weights?
700 mg to 740 mg
sam surveyed 200 students and recorded eye color and the gender of each student. of the 80 male students who were surveyed, 60 had brown eyes. if eye color and gender are independent, how many female students surveyed would be expected to have brown eyes?
90
a well designed experiment should have which of the following characteristics?: I. subjects assigned randomly to treatments; II. a control group or at least two treatment groups; III. replication
I, II, and III
I. a point with a large residual is an outlier; II. a point with high leverage has a y-value that is not consistent with the other y-values in the set; III. the removal of an influential point from a data set could change the value of the correlation coefficient. which of the above statements about a least-squares regression analysis is true?
III only
6 year old girls mean height = 40.6 inches and SD of 2.7 inches. aliyaah's height is .96 SD above the mean. her friend jayne is at the 93rd percentile of height distribution. at what percentile is aliyaah's height, and how does her height compare to jayne's height.
aliyaah's height is at the 83rd percentile of the distribution, and she is shorter than jayne.
measurements of water quality were taken from a river downstream from an abandoned chemical dumpsite. concentrations of a certain chemical were obtained from 9 measurements taken at the surface, 9 at mid-depth, and 9 at the bottom. what type of study was conducted, and what is the response variable of the study?
an observational study was conducted, and the response variable is the concentration of the chemical
a company determines the mean and standard deviation of the # of sick days taken by its employees in one year. which of the following is the best description of the standard deviation?
approximately the mean distance between the number of sick days taken by individual employees and the mean # of sick days taken by all employees
a car rental agency has two locations in a city. the boxplots below summarize the miles driven for one day of single-day car rentals at each location. based on the boxplots, which statement provides the best comparison of the two locations?
compared with location A, the miles driven for location B display more variability, and the median is greater
a store owner reports that the probability that a customer who purchases a lawn mower will also purchase an extended warranty is 0.68. which of the following is the best interpretation of the probability 0.68?
for all customers who purchase a lawn mower, 68% will also purchase an extended warranty
based on the scatterplots, for which gender does there appear to be evidence that the more time a lion cub spends playing, the sooner the cub is likely to begin hunting?
for female cubs only
gina's doctor told her that the standardized score (z-score) for her systolic blood pressure, as compared to the blood pressure of other women her age, is 1.50. which of the following is the best interpretation of this standardized score?
gina's systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age
the following bar chart shows the relative frequencies of students from each grade who participate in the community service activity. which of the following statements is supported by the bar chart?
grade 12 had the least relative frequency of participating students
as a part of the show, a green puppet and a yellow puppet served as the helper and the hinderer. for each baby, a coin was tossed to determine which color would serve which role. which of the following is the most important reason for the random assignment of color to role in the study?
if the same role is played by the same color puppet, the babies might show a preference for the color instead of a preference for the role
TEST 4: which of the following distinguishes an observational study from a randomized experiment?
in an observational study treatments are NOT randomly assigned, whereas in a randomized experiment treatments are randomly assigned
researcher, cell growth, strain types, replication, four lab technicians, etc. a statistician told the researcher that the design could be improved by controlling confounding variables. which of the following is potentially a confouding variable in this study?
lab technician
a researcher conducting a telephone survey is concerned about possible sources of bias. of the following, which is the best example of nonresponse bias?
many of the people selected to participate in the survey who do not respond might have opinions different from those who do respond
in driving a car, the events of driving over the speed limit and getting a ticket are
neither
the probability that a randomly selected visitor to a certain website will be asked to participate in an online survey is 0.40. avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey. is avery interpreting the probability correctly?
no because 0.40 represents probability in the long run over many visits to the site
I. random scatter in the residuals indicates a model with high predictive power; II. if two variables are very strongly associated, 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. which is true?
none
in a large set of data that are approximately normally distributed, R is the value in the data set that has a z-score of -1.00, S is the value of the first quartile, and T is the value of the 20th percentile. which of the following is correct order from LEAST to GREATEST for the values of r, s and t?
r, t, s
the histograms show the results for each region. the graph for which region displays data for level of interest with the least standard deviation?
region D
the table shows data that were collected from people who attended a certain high school basketball game and indicates the team each person rooted for and whether each of these people purchased food during the game. a person who attended the game will be selected at random. which of the following correctly interprets mutually exclusive events represented by the table?
rooting for the home team and rooting for the away team
a family would like to build a linear regression equation to predict the amount of grain harvested per acre of land on their farm. they subdivide their land into several smaller plots of land for testing and would like to select an explanatory variable they can control. which of the following is an appropriate explanatory variable that the family could use to create a linear regression equation?
the amount of fertilizer applied to each plot of land
an experiment will be conducted to determine whether children learn their multiplication facts better by practicing on flashcards or by practicing on a computer. children who volunteer for the experiment will be randomly assigned to one of the two treatments. after practice, the children will be given a test on their multiplications facts. why will it be almost impossible to conduct a double-blind experiment?
the child will know whether he or she used flashcards or the computer.
under which of the following conditions is it preferable to use stratified random sampling rather than simple random sampling?
the population can be divided into strata so that the individuals in each stratum as much alike as possible
at an educational conference attended by many teachers in the state, the staff members randomly selected 50 conference attendees and asked them how long they have been teaching. which of the following describes the sample and the population to which it would be most reasonable for the staff members to generalize the results?
the sample is the 50 conference attendees, and the population is all the conference attendees
a scatterplot of student height, in inches, versus corresponding arm length, in inches, is shown below. one of the points in the graph is labeled A. if the point labeled A is removed, which of the following statements would be true?
the slope of the least squares regression line increases and the correlation coefficient increases
which of the following statements must be true about the data sets A and B displayed in the histograms below?
the standard deviation of data set A is greater than the standard deviation of data set B
which of the following must be true about the 9 measurements, excluding the outlier, when compared with the 10 measurements?
the standard deviation of the 9 measurements is less than the standard deviation if the 10 measurements
chem- 75 mean & SD of 12; calc- 80 mean & SD of 8. a student scored 81 on the chemistry final and 84 on the calculus final. relative to the students in each respective class, in which subject did this student do better?
the student did equally well in each course
from 10 identical cuts of lamb, 2 are randomly selected to roast using each of the time-temperature combinations in the same oven. the quality of the finished product is evaluated for each roast. which of the following is true?
the two cuts that are being roasted for each time-temperature combination are an example of replication
a graph (not shown) of the selling prices of homes in a certain city for the month of april reveals that the distribution is skewed to the left. which of the following statements is the most reasonable conclusion about the selling prices based on the graph?
the value of maximum minus third quartile is less than the value of first quartile minus minimum
data were collected on 100 united states coins minted in 2018. which of the following represents a quantitative variable for the data collected?
the value of the coin
a tennis ball was thrown in the air. the height of the ball from the ground was recorded every millisecond from the time the ball was thrown until it reached the height from which it was thrown. the correlation between the time and height was computed to be 0. what does this correlation suggest about the relationship between the time and height?
there is no linear relationship between time and height
suppose a roadrunner has a total length of 59.0 cm and a tail length of 31.1 cm. based on the residual, does the regression model overestimate or underestimate the tail length of the roadrunner?
underestimate, because the residual is positive
TEST 1: which of the following shapes is NOT represented by one of the four distributions? (pictures not shown) *just memorize the answer*
uniform
list the sample space and tell whether the outcomes are equally likely. a family has two children; record the genders in order of birth
{BB, BG, GB, GG}, equally likely
