Cumulative Exam STATs (80%)
Without making any calculations, which distribution of data has the largest standard deviation?
1, 1, 1, 1, 4, 4, 7, 7, 7, 7
The final exam grade distribution for all students in the introductory statistics class at a local community college is displayed in the table, with A = 4, B = 3, C = 2, D = 1, and F = 0. Let X represent the grade for a randomly selected student from the class. What is the standard deviation of the distribution?
1.08
The bar graph below displays students' responses to the question "What caffeinated drinks do you consume?" Which of the following statements is correct?
All of the above.
An ice hockey team is considering changing their team name and mascot and would like to measure city support for the change. Which of the following methods would not provide a voluntary response sample?
At one of the team's games, a person surveys the first 50 people who arrive at the game.
A botanist wants to determine if a fertilizer is effective in the growth of plants. He randomly selects 100 of the same type of seedling and randomly assigns them to two groups: one that uses the fertilizer, and one that does not. He makes sure the plants all have the same amount of water, soil, and light for two months. At the end of two months, he measures the heights of the plants and finds that the ones receiving the fertilizer are significantly taller. Which of the following is a valid conclusion?
Inferences can be made for all plants, and the conclusion can be drawn that the fertilizer will help all plants grow taller.
Residents in a city are charged for water usage every three months. The water bill is computed from a common fee, along with the amount of water the customers use. The last water bills for 40 residents from two different neighborhoods are shown in the histograms below. Which of the following is a true statement comparing the water bills of the two neighborhoods?
More homes on Pine Road had water bills above $200 than on Front Street.
Manufacturers of tires report that car tires should be able to last an average of 50,000 miles. A new tire company produces a different type of tread and tests 100 randomly selected tires. This sample of 100 tires lasted an average of 51,500 miles. Assuming the new type of tread does not improve the mileage of the tire, 200 sample means were simulated and displayed on the dotplot. Using the dotplot and the sample mean mileage, is there convincing evidence that the new type of tread improves the mileage of the tire?
No, because a mean mileage of 51,500 or more occurred 14 out of 200 times, the mean mileage is not statistically significant. There is not convincing evidence the new type of tire tread improves mileage of the tire.
The president of a school club would like to purchase T-shirts for members of the club and asks members which size they would like to order. The results are shown in the histogram below. Which of the following is a true statement regarding the information shown in the histogram?
T-shirt size is categorical variable.
A school district wanted to compare ACT scores between two of its schools (school A and school B). The dotplots below summarize the ACT scores for simple random samples of 30 students from each school. The median score was 22 for both samples. Which of the following statements is true about the mean ACT for each sample?
The mean score for the sample from school A is greater than the mean score for the sample from school B.
One professional basketball player typically attempts eight free throws per game. Let X represent the number of free throws made out of eight. The distribution for X is shown in the table. Which of the following is the correct interpretation of P(X ≤ 3)?
The probability of the number of free throws made out of 8 is at most 3.
There are four blood types, and not all are equally likely to be in blood banks. 49% of donations are type O blood, 27% of donations are type A blood, 20% of donations are type B blood, and 4% of donations are type AB blood. A person with type A blood can safely receive blood transfusions of type O and type A blood. What is the probability that if 3 donations are made, all 3 of them can be safely used in a blood transfusion on someone with type A blood?
(0.27)3 + (0.49)3 = 0.1373
A local charity holds a carnival to raise money. In one activity, participants make a $3 donation for a chance to spin a wheel that has 10 spaces marked with the values 0, 1, 2, 5, and 10. The participant wins the dollar amount marked on the space on which the wheel stops. Let X represent the value of a spin. The distribution of X is given in the table. What is the median of the distribution?
1
A 10-item statistics quiz was given to 30 students. The table below gives the scores received along with the corresponding frequencies. What was the median score on the quiz?
9
A website lists homes for sale in a suburban town. The site provides information including neighborhood, selling price, age of the home (in years), number of bedrooms, and whether the home has a garage. Which of the variables is a categorical variable?
Neighborhood
The stemplot below displays the times, in seconds, for 25 students to run 100 meters. Are there any outliers?
No, there are no outliers.
To survey clients at a massage-therapy spa, a researcher alphabetically lists all of the customers the spa had last month. The researcher sends a survey to the 13th person on the list (with the number 13 being randomly chosen), then surveys every 20th customer after that. Which sampling method was used?
Systematic Random sampling
The parallel boxplots below display the bag weights of two different brands, A and B, of granola. Which statement best compares the variability of the distributions for the bag weights?
The bag weights for brand A have less variability than the bag weights for brand B.
A six-sided number cube is rolled and the proportion of 3s is calculated. The graph shows the long-run relative frequency of 100 rolls of this die. Which conclusion can be drawn from this graph?
The long-run frequency of rolling a 3 appears to be about 0.17.
According to a recent survey of adults, approximately 62% carry cash on a regular basis. The adults were also asked if they have children. Of the 46% who have children, 85% carry cash on a regular basis. Is carrying cash independent from having children in this sample?
Yes, P(carry cash) = P(carry cash|have children).
The president of the student council wants to survey the student population about parking. She decides to take a random sample of 100 of the 1,020 students at the school. She gets an alphabetical list of the students, and numbers them from 0001 to 1020. Then, using a random number table, and starting at a random line, she selects 100 unique numbers between 0001 and 1020. Is this a simple random sample?
Yes, because each student and sample of 100 has the same chance of being selected.
An English test has 50 multiple-choice questions, each with five answer choices and one correct answer. A student guesses each answer choice randomly. Let X represent the number of questions answered correctly. What is the shape of the probability histogram of X?
approximately symmetric
The dotplot below displays the difference in scores for 18 games between a high school soccer team and its opponent. Which of the following best describes the shape of the distribution?
skewed to the left
A ski resort claims that there is a 75% chance of snow on any given day in January and that snowfall happens independently from one day to the next. A family plans a four-day trip to this ski resort in January. Let X represent the number of days it snows while the family is there. What are the mean and standard deviation of X?
ux=3, ox= 0.87
Residents in a city are charged for water usage every three months. The water bill is computed from a common fee, along with the amount of water the customers use. The last water bills for 40 neighborhood residents are displayed in the histogram below. Which of these correctly describes the shape of the distribution of water bills?
skewed left
A standard deck of 52 playing cards contains 13 cards in each of four suits: hearts, diamonds, clubs, and spades. Four cards are drawn from the deck at random. What is the approximate probability that exactly three of the cards are diamonds?
4%
A study of traffic violations on a busy highway finds that the number of tickets for speeding written by officers tends to decrease on rainy days. A police sergeant explains that driver behavior could be a confounding variable. Which statement best explains the confounding variable in this study?
Drivers may drive more carefully on rainy days, so the number of speeding tickets decreases.
Two students created a game of dice. They determined that each roll would add the value of the die if it was an odd number. If the roll was even, it would subtract the value of the die. (For example, a roll of 2 would subtract two points, but a roll of 3 would add three points.) What is the expected value for this game?
-0.5
There are 4 blood types, and not all are equally likely to be in blood banks. 49% of donations are type O blood, 27% of donations are type A blood, 20% of donations are type B blood, and 4% of donations are type AB blood. A person with type A blood can safely receive blood transfusions of type O and type A blood. If three donations are made, what is the probability that at least 1 of them can be safely used in a blood transfusion on someone with type A blood?
0.0138
A security alarm requires a four-digit code. The code can use the digits 0-9 and the digits cannot be repeated. What is the approximate probability that the code only contains odd numbers?
0.02381
A medical clinic is randomly selecting three staff members to attend a conference. The clinic employees include 7 nurses, 3 doctors, and 4 office staff. What is the probability that three nurses are selected to attend the conference?
0.10
Some randomly selected high school students were asked to name their favorite sport to watch. The table displays the distribution of results. What is the probability that a student chose football given that they like watching sports?
0.23
The probability that a mature hen will lay an egg on a given day is 0.80. Hannah has 12 hens. What is the probability that 10 of the 12 hens will lay eggs on a given day?
0.28
A survey of high schools offering honors classes to ninth graders reveals that 38% of the high schools offer no honors classes, 12% offer one honors class, 25% offer two honors classes, 20% offer three honors classes, and 5% offer four honors classes. A high school is selected at random. What is the probability that it offers an even number of honors classes?
0.30
During final exam weeks, many college students exercise to fuel their study sessions. Data from a recent survey are shown in the Venn diagram. Let M be the event that the student exercises in the morning and let A be the event that the student exercises in the afternoon. What is the probability that a randomly chosen college student exercises in the morning or the afternoon, but not both?
0.39
A local charity holds a carnival to raise money. In one activity, participants make a $3 donation for a chance to spin a wheel that has 10 spaces with the values, 0, 1, 2, 5, and 10. Whatever space it lands on, the participant wins that value. Let X represent the value of a random spin. The distribution is given in the table. What is the probability that the value is 0?
0.4
Insurance company executives surveyed 200 young adults about their first motor vehicle. The results of the survey are given in the following two-way table. A survey participant is randomly selected. Let F be the event that the participant's first motor vehicle had four cylinders and let C be the event that the participant's first motor vehicle was a car. What is the value of P(F or C)?
0.80
A car wash has three different types of washes: basic, classic, and ultimate. Based on records, 45% of customers get the basic wash, 35% get the classic wash, and 20% get the ultimate wash. Some customers also vacuum out their cars after the wash. The car wash records show that 10% of customers who get the basic wash, 25% of customers who get the classic wash, and 60% of customers who get the ultimate wash also vacuum their cars. The probabilities are displayed in the tree diagram. What is the probability that a randomly selected customer purchases the basic or classic car wash if they vacuum their car?
0.80???
At a carnival game, the chance of winning a prize is 0.45. Kylee plays the game 3 times. Using the table, what is the probability that she wins at least 1 prize?
0.83
Student body elections are coming up and there are a lot of options. There are 3 candidates for president, 4 for secretary, and 10 for mascot. Suppose a student were to fill out their ballot by randomly picking a candidate or abstaining for each position. Each outcome in the sample space for the random ballots is equally likely. What is the probability of each outcome in the sample space?
1/120
A farmer sows 100 seeds of a new type of corn and wants to quickly determine the yield, or total number of ears of corn, for the crop when it has matured. He decides to take a simple random sample of 10 corn plants. He labels the 100 plants 00-99. Refer to the given line from a random number table. Which numbers represent the sample of 10 corn plants?
58, 16, 00, 96, 95, 38, 39, 94, 04, 32
Marleny is creating a game of chance for her family. She has 5 different colored marbles in a bag: blue, red, yellow, white, and black. She decided that blue is the winning color. If a player chooses any other color, they lose 2 points. How many points should the blue marble be worth for the game to be fair?
8
A city official would like to know if there is public support for increasing funding for arts programs. To collect data, the city official stands outside a concert hall after a show and surveys the first 20 people to exit about their opinion of raising funds for the arts. Which of the following best describes any bias that may arise from the results?
Because those in the sample generally support the arts, the city official may overestimate support for raising funds.
People of different ages were asked the question "Do you listen to audiobooks?" The frequency table displays the percentage of "yes" responses for different age groups. Would it be appropriate to display the data with a pie chart?
No, because the data display the percentage of time spent by each age group, not a relative frequency compared with the whole.
An experiment is proposed to measure the effectiveness of a brand of sunscreen. Adult volunteers are randomly assigned to one of two brands of sunscreen and asked to enjoy a normal day at the beach. Each volunteer is asked to report back to the administrators after two hours, at which time both arms are assessed for sun exposure. Which statement describing this experiment is true?
The brands of sunscreen are the explanatory variables.
The side-by-side dotplot below displays the arm spans, in centimeters, for two classes. Which statement is NOT true?
The mean arm span appears to be similar for the two classes.
The parallel histograms below display the heights of men in each of two countries. Which of the following statements is not true?
The range for the distribution of men's heights is larger in country B.
A worker at the local Department of Motor Vehicles (DMV) claims that 60% of teenagers smile in their driver's license photo. In a random sample of 10 teenagers from last month's new driver's licenses, only 4 of them were smiling in their photos. To see how unusual this sample is, 100 simulated trials were conducted under the assumption that 60% of teenagers smile for their driver's license photo. Based on the dotplot of the simulation results and the random sample from last month's new driver's licenses, which conclusion can be drawn?
There is about an 8% chance that 4 or fewer teenagers smiled for their photo. This is not unusual and is not convincing evidence that the true probability is less than 60%.
A township supervisor hopes to improve the current recycling program by having residents separate their recycled materials by type. For example, glass and plastic materials would be placed into separate recycling containers. To measure community support for a change to the recycling program, the supervisor visits a busy shopping area and asks randomly selected residents to respond to the following question: "Do you agree that responsible citizens would separate their recycled items by type of material?" What type of bias could be present in the survey results and what is a likely direction of the bias in estimating community support for the change to the recycling program?
This is question wording bias. The survey overestimates community support for change to the recycling program.
Many delivery trucks feature a "How Am I Driving?" sticker on the rear bumper, along with a phone number. This sticker allows drivers to report erratic driving by the truck driver or offer a compliment if they like. A dispatcher at the trucking station accepts calls and records information from those who call the phone number. The dispatcher reports that in the past month, 218 calls were received. Of those calls, 178 reported negative driving behaviors by the truck drivers. How might this data-collection method produce bias in obtaining an estimate of all drivers who are satisfied with the company's truck drivers?
This sample may lead to voluntary response bias because drivers can choose to call the phone number and register an opinion.
A statistics teacher has 4 periods of introductory statistics. She wants to get students' opinions on a new homework policy. To get a sample, the teacher groups the students by their class performance (A students, B students, etc.). Then she randomly selects 3 students from each class performance group to survey. Which sampling method was used?
stratified random sampling
