Stats Fall Final

The sale bin in a clothing store contains an assortment of t-shirts in different sizes. There are 9 small, 7 medium, and 4 large shirts. Alan is looking for a large shirt. He starts grabbing shirts one at a time and checking the size. After he checks each shirt, 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 meterologist's estimates, approximately what is the propability that a future tropical storm will orignate in the Pacific Ocean and be classified as major?

0.170

At a California college, 22% of students speak Spanish, 5% speak French, and 3% speak both languages. What is the probability that a student chosen at random from the college speaks Spanish but not French?

0.19

Based on the approximation, what is the probability that at least 1 of the next 4 costumers who go to the service department will ask for help finding an item?

1 - (3/4)^4

The caffeine content of 8-ounce cans of a certain cola drink is approximately normally distributed with mean 33 milligrams (mg). A randomly selected 8-ounce can containing 35 mg of caffeine is 1.2 standard deviations above the mean. Approximately what percent of 8-ounce cans of the cola have a caffeine content greater than 35 mg?

12%

Scientists estimate that the distribution of the life span of the Galápagos Islands giant tortoise is approximately normal with mean 100 years and standard deviation 15 years. Based on the estimate, which of the following is closest to the age of a Galápagos Islands giant tortoise at the 90th percentile of the distribution?

120 years

One student from the school will be selected at random. What is the probability that the student is in the age-group of 6 to 8 years given that teh selected student responded joy?

28/89

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

The histogram shows the distribution of heights, in inches, of 100 adult men. Based on the histogram, which of the following is closest to the interquartile range, in inches, of the distribution?

5

Sam surveyed 200 students at a school and recorded the 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

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.

In a certain school district, students from grade 6 through grade 12 can participate in a school-sponsored community service activity. 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.

A well-designed experiment should have which of the following characteristics?

I, II, and III

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.

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.

A high school science teacher has 78 students. Of those students, 35 are in the band and 32 are on a sports team. There are 16 students who are not in the band or on a sports team. One students from the 78 students will be selected at random. Let event B represent the event of selecting a student in the band, and let event A represent the event of selecting a student on a sports team. Are A and B mutually exclusive events.

No, because P(BnS) = 5/78

Staff members of a high school newspaper want to obtain an estimate of the average number of years teachers in the state have been teaching. At the educational conference attended by many teachers in the state, the staff members randomly selected 50 conference attendees and asked the attendees 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 staf members to generalize the results?

The sample is the 50 conference attendees, and the population is all conference attendees.

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.

A new restaurant is interested in determining the best time-temperature combination for roasting a five-pound cut of lamb. The times to be tested are 45 minutes, 60 minutes, and 90 minutes at temperatures of 350 degrees Farenheit and 425 degrees Farenheit for each time, with the exception of the 90 minute-425 degree combination.... 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.

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

Which of the following is the correct order from least to greatest for the values of r, s, and t ?

r, t, s

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

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%

A candy company produces individually wrapped candies. The quality control manager for the company believes that the weight of the candies is approximately normally distributed with mean 720 milligrams (mg).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

A company determines the mean and standard deviation of the number 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 number of sick days taken by all employees

A researcher wanted to study the effects of a certain chemical on cell growth. The chemical was applied at two different doses, high and low, to two different cell types, strain A and strain B. Each combination of does and cell type was to be replicated ten times.... Which of the following is potentially a confounding variable in this study?

Lab technician

A marketing firm obtained random samples of 20 people in five regions of the country to investigate the level of interest in a new product. People in the sample were asked to rate their level of interest on a scale from 1 to 10, with 1 being the least amount of interest and 10 being the greatest. 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

At a large airport, data were recorded for one month on how many baggage items were unloaded from each flight upon arrival as well as the time required to deliver all the baggage items on the flight to the baggage claim area. A scatterplot of 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.

A local real estate magazine used the median instead of the mean when it reported the SAT score of the average student who attends Groveland High School. A graphical display of SAT scores of students who attend Groveland High School indicated that the data were strongly skewed to the right. 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.

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 are as much alike as possible.

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 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.

The distributions of four variables are shown in the following histograms. Which of the following shapes is NOT represented by one of the four distributions?

Uniform

For flights from a particular airport in January, there is a 30 percent chance of a flight being delayed because of icy weather.... 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 cars are white, 30 cars are red, and 20 cars are silver. One car will be selected at random from the parking lot. If each car in the parking has only one color, which of the folloing cannot be the probability that the selected car will be green.

0.6

Opinion-polling organizations contact their respondents by sampling random telephone numbers. Assume that interviewers can now reach about 71% of US 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 catched a T-shirt. What is the probability that she will catch a T-shirt that is not a size small?

0.80

A police officer is using a radar device to check motorist's speeds. Prior to beginning the speed check, the officer estimates that 40 percent of motorists will be driving more than 5 miles per hour over the speed limit. Assuming that the police officer's probability is correct, what is the probability that among 4 randomly selected motorists, the officer will find at least 1 motorist driving more than 5 miles per hour over the speed limit?

0.8704

Ninety percent of the people who have a particular disease will have a positive result on a given diagnostic test. Ninety percent of the people who do not have the disease will have a negative result on this test. If 5 percent of a certain population has the disease, what percent of that population would test positive for the disease?

14%

Shalise competed in a jigsaw puzzle competition where participants are timed on how long they take to complete puzzles of various sizes. Shalise completed a small puzzle in 75 minutes and a large jigsaw puzzle in 140 minutes. For all participants, the distribution of completion time for the small puzzle was approximately normal with mean 60 minutes and standard deviation 15 minutes. The distribution of completion time for the large puzzle was approximately normal with mean 180 minutes and standard deviation 40 minutes. Approximately what percent of the participants had finishing times greater than Shalise's for each puzzle?

16% on the small puzzle and 84% on the large puzzle

The weight of adult male grizzly bears living in the wild in the continental United States is approximately normally distributed with a mean of 500 pounds and a standard deviation of 50 pounds. The weight of adult female grizzly bears is approximately normally distributed with a mean of 300 pounds and a standard deviation of 40 pounds. Approximately, what would be the weight of a female grizzly bear with the same standardized score (z-score) as a male grizzly bear with a weight of 530 pounds?

324 pounds

Which of the following can be used to show a cause-and-effect relationship between two variables?

A controlled experiment

Dairy farmers are aware there is often a linear relationship between the age, in years, of a dairy cow and the amount of milk produced, in gallons per week. 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.

The distribution of heights of 6-year-old girls is approximately normally distributed with a mean of 46.0 inches and a standard deviation of 2.7 inches. Aliyaah is 6 years old, and her height is 0.96 standard deviation above the mean. Her friend Jayne is also 6 years old and is at the 93rd percentile of the 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 of the water, 9 measurements taken at mid-depth of the water, and 9 measurements taken at the bottom of the water. 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.

In a certain school, students can choose whether to eat in the school's cafeteria. A reporter working for the school's newspaper polled students on their reactions to changes in the menu at the cafeteria. Which of the following statements is true?

Because students self-elected whether to eat in the cafeteria, the sampling method might be biased and the sample might not be representative of all the students in the school.

At a local ice-cream store, 210 people were surveyed on whether they preferred eating ice cream from a cone or a cup. Of the 210 people surveyed, 70 were adults and 140 were children. Of the responses, 150 indicated the cone as the preferred method of eating ice cream. For those surveyed, there was no association between age and preferred method of eating ice cream. Which of the following tables shows the distribution of responses?

C

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 botanist found a correlation between the length of an aspen leaf and its surface area to be 0.94. 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 value of 0.94, it is possible that the relationship could still be better represented by a nonlinear model.

The SC Electric Company has bid on two electrical writing jobs. If the owner's beliefs are correct, which of the following statements must be true concerning event A and event B?

Event A and B are not mututally exlcusive and are not independent

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 aslo purchase an extended warranty.

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

Which of the above statements about a least-squares regression analysis is true?

III only

As part of the show, a green puppet and a yellow puppet served as the helper and 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.

Which of the following distinguishes an observational study from a randomized experiment?

In an observational study a random sample is always taken from the population, whereas in a randomized experiment volunteers are always used.

In driving a car, the events of driving over the speed limit and getting a speeding ticket are

Neither

Which is true?

None

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 with flash cards 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 multiplication facts. Why is it impossible to conduct a double-blind experiment?

The child will know whether he or she used flash cards or the computer.

As part of a science experiment, a student recorded 10 measurements of the temperature of a liquid. One of the measurements was an outlier when compared with the other 9 measurements. Which of the following must be true about the 9 measurements, excluding the outlier, when compared with the 10 measurements? (Note: An outlier is any number that is greater than the upper quartile or less than the lower quartile by at least 1.5 times the interquartile range.)

The standard deviation of the 9 measurements is less than the standard deviation of the 10 measurements.

At a college the scores on the chemistry final exam are approximately normally distributed, with a mean of 75 and a standard deviation of 12. The scores on the calculus final are also approximately normally distributed, with a mean of 80 and a standard deviation 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.

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.

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