A Statistics Quiz

JT has two jobs. He mows yards and washes cars in his neighborhood. Let X represent the amount of weekly earnings for mowing yards, and let Y represent the amount of weekly earnings for washing cars. The mean of X is $60, and the mean of Y is $35. Which answer choice correctly calculates and interprets the mean of the sum, S = X + Y?

D) ; JT can expect to earn $95, on average, in a typical week.

Lynnetta gets paid weekly for completing household chores. The amount of money she earns for doing dishes, D, is approximately Normally distributed with a mean of $53 and a standard deviation of $3.60. The amount of money she earns for doing laundry, L, is approximately Normally distributed with a mean of $47 and a standard deviation of $4.10. Assume that D and L are independent random variables. What is the probability that Lynnetta will earn more than $110 in a randomly selected week?

A) 0.034

Two machines, X and Y, produce earbuds. Let X represent the diameter of an earbud produced by machine X, and let Y represent the diameter of an earbud produced by machine Y. X has a mean of 14 mm with a standard deviation of 0.6 mm, and Y has a mean of 15.2 mm with a standard deviation of 0.2 mm. Which answer choice correctly calculates and interprets the mean of the difference, D = X - Y?

A) = -1.2; earbud manufacturers can expect the difference in the diameter of earbuds produced from machines X and Y, on average, to be -1.2 mm.

Graduation rate is one measure used to compare colleges in national publications. One such publication compared semester tuition against graduation rate, defined as the percentage of students who graduate within four years. The value of r for the scatterplot is 0.856. How would the correlation change if the graduation rate was plotted on the x-axis and tuition plotted on the y-axis?

A) The correlation would stay the same.

The weekly sales results of three sales teams are displayed below.

A) The weekly sales results of three sales teams are displayed below.

Does eating a mint affect a person's taste buds? To answer this question, students were randomly placed into two groups. One group had to eat a mint, and the other did not. Then all the students were given a cup that had one of two brands of ice tea. Students were asked to guess which brand of ice tea they had. The results are displayed below.

A) There is an association because the distribution of correct guesses differs among the mint groups.

Customers in a coffee shop were asked if they prefer caffeinated or decaffeinated coffee and if they prefer their coffee with or without milk. highThe results are displayed below.

A) There is an association because the distribution of milk preference differs among the types of coffee.

Three car dealerships were surveyed about the number of vehicles that were sold with automatic or manual transmissions. The results are displayed below.

A) There is an association because the distribution of purchasing an automatic differs among the dealerships.

In the decathlon event at large track meets, male athletes compete in a total of 10 events. Their combined performance in each of the events is used to determine the winner. Two of the events are the 200-meter dash and the javelin throw. For 12 athletes at a large international competition, performances in these events are recorded and placed in a scatterplot. The performance for one athlete from Latvia is labeled in the graph. How does this point influence the correlation of the scatterplot?

A) This data point weakens the correlation.

Manufacturers of tires report that 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 52,000 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

A) Yes, because a mean mileage of 52,000 or more occurred only 7 out of 200 times, the mean mileage is statistically significant. There is convincing evidence the new type of tire tread improves mileage of the tire.

Car rideshare services are a popular option for people needing to move about in large cities. The scatterplot shows the distances and fares, in dollars, for an adult living in a city over a month period. The value of r for the scatterplot is 0.950. Which of the labeled points weakens the overall association between distance and fare?

A) point A

Alicia and Bennie have decided to play a game. They each draw as many flowers on paper as they can within one minute, repeating this game many times. The number of flowers Alicia draws and the number of flowers Bennie draws are independent. The number of flowers Alicia draws within 1 minute, A, is approximately Normally distributed with a mean of 38 flowers and a standard deviation of 1.8 flowers. The number of flowers Bennie draws in 1 minute, B, is approximately Normally distributed with a mean of 41 and a standard deviation of 2.6 flowers. Let D represent the difference, A - B, in the number of Alicia's and Bennie's flowers drawn in 1 minute. What is the probability that Alicia draws fewer flowers than Bennie in any 1 minute?

C) 0.829

Randi and Leah are studying together for an exam. Let X represent the number of hours Randi spends studying nightly, and let Y represent the number of hours Leah spends studying nightly. The mean of X is 4.5 hours with a standard deviation of 1.1 hours, and the mean of Y is 3.7 hours with a standard deviation of 1.8 hours. Assuming these are independent random variables, which answer choice correctly calculates and interprets the standard deviation of the sum, S = X + Y?

C) ; Randi and Leah can expect the total number of hours spent studying to vary by approximately 2.1 hours from the mean.

Two companies, A and B, package snack-size bags of cashews. Let X represent the weight of the packages from company A, and let Y represent the weight of the packages from company B. The mean of X is 2.4 ounces with a standard deviation of 0.3 ounces, and the mean of Y is 1.8 ounces with a standard deviation of 0.5 ounces. Assuming these are independent random variables, which answer choice correctly calculates and interprets the standard deviation of the sum, S = X + Y?

C) = 0.58; companies A and B can expect the total weight of packages to vary by approximately 0.58 ounces from the mean.

There are frogs and koi in a pond, and the number of frogs and the number of koi in the pond are independent. Let X represent the number of frogs in any given week, and let Y represent the number of koi in any given week. X has a mean of 28 with a standard deviation of 2.7, and Y has a mean of 15 with a standard deviation of 1.6. Which answer choice correctly calculates and interprets the standard deviation of the difference, D = X - Y?

C) = 3.1; this pond can expect the difference of frogs and koi to vary by approximately 3.1 from the mean.

Three car dealerships were surveyed about the percentage of vehicles on their lot with automatic or manual transmissions. The results are displayed below.

C) Dealership C has the highest percentage of automatic transmissions.

A florist wants to determine if a new additive would extend the life of cut flowers longer than the original additive. The florist randomly selects 20 carnations from the ones recently delivered by the greenhouse and randomly assigns 10 to the new additive and 10 to the original additive. After three weeks, 6 carnations placed in the new additive still looked healthy and 2 carnations placed in the original additive still looked healthy. The proportion of healthy carnations with the new additive was significantly greater than the proportion of healthy carnations with the original additive. Which of the following is a valid conclusion?

C) It can be concluded that the new additive caused the extended life of the cut flowers, and this inference can only be applied to the carnations from the greenhouse.

Fuel efficiency, measured in miles per gallon, is a feature often considered by shoppers looking for a new car. The scatterplot shows the vehicle weight of 15 car models in pounds, plotted against their highway fuel efficiency. Which of the following is a reasonable value for r, given the relationship shown in the scatterplot?

B) -0.898

Soledad and Tania are both high school students. The number of texts Soledad sends daily, S, is approximately Normally distributed with a mean of 100 and a standard deviation of 6 texts. The number of texts Tania sends daily, T, is approximately Normally distributed with a mean of 108 and a standard deviation of 8.1 texts. Assume that S and T are independent random variables. Let D = S - T. What is the probability that Soledad sends more texts on a randomly selected day?

B) 0.214

A consumer agency wants to determine which of two laundry detergents, A or B, cleans better. Fifty pieces of fabric are subjected to the same kinds of stains (grass, mud, coffee). Then 25 pieces are randomly assigned to be cleaned with detergent A, and the remaining 25 pieces are cleaned with detergent B. After being laundered, the pieces of fabric are rated on a scale of 1-10, with 1 being the least clean to 10 being the most clean. The mean rating for detergent A is found to be significantly less than the mean rating for detergent B. Which of the following is a valid conclusion?

B) Inferences cannot be made about the population of fabric from which the pieces were chosen; however, the conclusion can be made that detergent B cleans better that detergent A for these 50 pieces of fabric.

A manufacturer of bottled tea runs a promotion in which consumers can win a free bottle of tea if the cap of the bottle says "Winner." The manufacturer claims that 1 in 5 bottles is a winner. A store owner notices that several of the first bottles of tea sold were winners. Suspecting the manufacturer's claim is false, the store owner decides to randomly select 10 bottles of tea from the next shipment from the manufacturer. She is again surprised when 4 of the bottles are winners. Assuming the manufacturer's claim is true, she simulates 100 values of selecting winners in 10 bottles. The dotplot displays these simulated proportions. Using the dotplot and the proportion of winners in the store owner's sample, is there convincing evidence that the manufacturer's claim is wrong?

B) No, because a proportion of 0.4 or more occurred 25 out of 100 times, the sample proportion of winners is not statistically significant and there is not convincing evidence that the manufacturer's claim is false.

Does eating a mint affect a person's taste buds? To answer this question, students were randomly placed into two groups. One group had to eat a mint, and the other did not. Then all the students were given a cup that had one of two brands of ice tea. Students were asked to guess which brand of ice tea they had. The results are displayed below.

B) Students who did not eat a mint were more accurate guessers.

The weekly sales results of three sales teams are displayed below.

B) Team B has its highest sales toward the end of the week.

The scatterplot illustrates the relationship between two quantitative variables. Which of the following is an accurate description of the scatterplot?

B) This relationship contains two unusual points.

A marathon runner is interested in split times, which is the time to complete the first half of the race and the second half of the race. She collects split times for 10 runners and summarizes the data in the table. The equation of the least-squares regression line is ŷ = -51.0 + 1.44x, where ŷ is the time (in minutes) to finish the second half of the race and x is the time (in minutes) to finish the first half. Which shows the residual plot?

C

A florist wants to determine if a new additive would help extend the life of cut flowers longer than the original additive. The florist randomly selects 20 carnations and randomly assigns 10 to the new additive and 10 to the original additive. After three weeks, 5 carnations placed in the new additive still looked healthy, and 3 carnations placed in the original additive still looked healthy. The difference in proportions (new - original) for the carnations that still looked healthy after three weeks was 0.2. Assuming there is no difference in the additives, 200 simulated differences in sample proportions are displayed in the dotplot. Using this dotplot and the difference in proportions from the samples, is there convincing evidence that the new additive was more effective?

C) No, because a difference in proportions of 0.2 or more occurred 41 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.

A nutritionist collects data from 25 popular breakfast cereals. For each cereal, the number of calories per serving is plotted on the x-axis against the number of milligrams of sodium on the y-axis. The value of r for the resulting scatterplot is 0.83. Which of the following is a correct interpretation of this value?

C) There is a positive relationship between calories and sodium. The relationship is strong.

A health organization collects data on hospitals in a large metropolitan area. The scatterplot shows the relationship between two variables the organization collected: the number of beds each hospital has available and the average number of days a patient stays in the hospital (mean length of stay). Which of these statements best describes the relationship between the variables shown in the scatterplot?

C) There is a positive relationship between number of beds and lengths of stay.

Some students were surveyed about their eye color and their favorite color. The results are displayed below.

C) There is no association because the distribution of favorite colors is the same among the eye-color groups.

To investigate the influence of distracted driving, 13 volunteers were asked to participate in a study involving a driving simulator. The participants drove at a safe speed but were told to stop the car at a random moment during the simulation. The scatterplot shows the reaction time and the simulated car's stopping distance, in feet, for each volunteer. Which point most likely decreases the correlation shown in the scatterplot?

C) This data point weakens the correlation.

A book publisher publishes both fiction and nonfiction books. Let F represent the number of words, per chapter, for fiction books, and let N represent the number of words, per chapter, for nonfiction books. The standard deviation of the total amount, S = F + N, is 195.3 words. What is the interpretation of this value?

C) This publisher can expect the total number of words per chapter to vary by approximately 195.3 words from the mean.

A sports analyst is interested in the relationship between the number of three-point shots players attempt in a game and the number of points scored. To investigate the relationship, he collects a simple random sample of 15 games and records the number of three-point shots attempted and the total number of points scored. He finds the equation of the least-squares regression line to be ŷ = 65.7 + 0.729x, where ŷ is points scored and x is the number of three-point shots attempted. The residual plot is shown. Based on the residual plot, is the linear model appropriate?

C) Yes, there is no clear pattern in the residual plot

A florist wants to determine if a new additive would extend the life of cut flowers longer than the original additive. The florist randomly selects 20 carnations from the ones recently delivered by the greenhouse and places the first 10 in water with the new additive and remaining 10 in water with the original additive. After three weeks, 6 carnations placed in the new additive still looked healthy and 2 carnations placed in the original additive still looked healthy. The proportion of healthy carnations with the new additive was significantly greater than the proportion of healthy carnations with the original additive. Which of the following is a valid conclusion?

D) Conclusions about cause and effect for the additives cannot be made, because the florist took a random sample of 20 carnations; and, inferences cannot be made about the population of carnations at the greenhouse, because the carnations were not randomly assigned to the treatments.

One statistic used to measure a country's wealth is its gross domestic product (GDP). A higher GDP indicates greater wealth in the country. A researcher compared the GDP per person for 12 countries with the life expectancy of that country. The data for the 12 countries are shown in the scatterplot. The value of r for the scatterplot is 0.608. Which of the following statements accurately describes the relationship shown in the scatterplot?

D) Countries with higher GDPs tend to have higher life expectancies.

A pharmaceutical company develops a new generation of blood pressure medication that may also help with cholesterol. The research and development department advertises in the local papers and online for volunteers who already take blood pressure medication to participate in a study for the new medication. Two hundred people volunteer, and their current blood pressure along with their cholesterol levels are measured. The first 100 volunteers are assigned to the new generation of blood pressure medication, and the next 100 are assigned to the original medication. At the end of the study, the subjects' blood pressures and cholesterol levels are measured. The group with the new medication is found to have significantly lower overall blood pressure than the original medication group. It was also determined that the new medication did not significantly lower cholesterol levels. Which of the following is a valid conclusion?

D) Inferences cannot be made about all blood pressure patients, and the conclusion cannot be made that the new medication lowers blood pressure more effectively than the original medication for patients taking blood pressure medication.

A botanist wants to determine if a fertilizer is effective in the growth of plants. He selects the first 100 plants of the same type of seedling from a greenhouse and assigns the first 50 to the group that uses the fertilizer and remaining seedlings to the group that does not use fertilizer. 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?

D) Inferences cannot be made for these types of plants, and the conclusion cannot be drawn that the fertilizer will help these types of plants grow taller.

An official for a regional baseball league examines attendance data for teams in the league. For each team in the league, the number of losses and the average game attendance are shown in the scatterplot. The value of r for the scatterplot is -0.847. Which statement best describes the association shown in the scatterplot?

D) Losses and attendance have a strong, negative association.

An entertainment reporter examines the average ticket prices of Broadway shows, comparing them to the number of total performances the shows have had. A resulting scatterplot shows a strong, positive relationship. The value of r for the scatterplot is 0.763. Which statement best explains the relationship between the variables?

D) More popular shows have higher ticket prices and offer more performances.

A company that manufactures golf balls produces a new type of ball that is supposed to travel significantly farther than the company's previous golf ball. To determine this, 40 new-style golf balls and 40 original-style golf balls are randomly selected from the company's production line on a specific day. A golf pro randomly selects a ball, not knowing which type is chosen, and hits it. The difference in mean distances traveled (new - original) for the samples was 4.9 feet. Assuming there is no difference in distance traveled between the two types of golf balls, 200 simulated differences in sample means are displayed in the dotplot. Using the dotplot and the difference in mean distances from the samples, is there convincing evidence that the new golf ball travels farther than the original golf ball?

D) No, because a difference in mean distances of 4.9 feet or less occurred 194 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence the new golf ball travels farther than the original golf ball.

A teacher tells her students that a large jar of marbles contains 55% red marbles. Students randomly select a sample of 40 marbles and determined the proportion of red marbles. One sample contained 18 red marbles. Assuming the teacher's claim is true, 100 simulated proportions are displayed in the dotplot. Using the dotplot and sample proportion, is there convincing evidence that the teacher's claim is false?

D) No, because a proportion of 0.45 or less occurred 16 out of 100 times, the sample proportion of red marbles is not statistically significant and there is not convincing evidence that the teacher's claim is false.

Tonya and Emily each have an online jewelry store. Let T represent the amount of money Tonya earns daily, and let E represent the amount of money Emily earns daily. The mean difference, D = T - E, of the amount of money that Tonya and Emily earn on a typical day is $312. What is the correct interpretation of this value?

D) On average, Tonya makes $312 more than Emily on a typical day.

A group of high school students were surveyed about their handedness and their favorite sport. The results are displayed below.

D) The percentage of people who prefer football is approximately the same for the right- and left-handed groups.

A group of high school students were surveyed about their handedness and their favorite sport. The results are displayed below.

D) There is no association because the distribution of sport preference is approximately the same among the handedness groups.

A health organization collects data on hospitals in a large metropolitan area. The scatterplot shows the relationship between two variables the organization collected: the number of beds each hospital has available and the average number of days a patient stays in the hospital (mean length of stay).

D) the hospital with 310 beds