Unit 6: Studies in Social Science

18. Sound waves from 2 musical instruments are recorded, as shown in the image. What is the difference between the sound created? How do you know?

B is louder because the amplitude is larger.

5. Doctors put a group of women preparing to run their first marathon in the same running group. All of the women were mothers. Which question would best be answered by conducting an experimental study of these women?

How does age affect the amount of time needed to complete the marathon?

1. Which question would best be answered by conducting an experimental study?

How does spraying calcium on apple trees once a month during the growing season affect fruit production?

34. A large health care system gave all nurses a flat wage increase. A union representative sampled 50 nurses and found that the mean increase in total wages was 5.2% with a standard deviation of 1.61. Using a 95% confidence interval, which statement from the union best describes the wage increase for all nurses in the system?

NOT The average wage increase for nurses in the system was between 3.6% and 6.8%.

14. An architect designs a wheelchair ramp for a historical building. The entry way is a level platform at the top of stairs that are 3 meters above ground level and extend 4 m out from the building. There is an obstacle 25m from the stairs, and the city code for ramps limits the incline angle to 6∘. Is there sufficient distance for a ramp within this limit? How do you know?

NOT Yes, because the ratio of 425 is less than tan6∘

7. Suppose a local university used an observational study to collect information from a sample group to learn about the university's entire student population. Which statement is true about the study?

No treatment is applied to the students in the study.

2. Which statement is true about an observational study?

No treatment is applied to the subjects in the study.

1. A marine biologist monitors a coral reef and determines the coral is dying at a rate that is 12.5% more than its growth rate each year. She estimates that the current population of live coral will be gone in 15 years. Is this an accurate prediction?

No, because after 15 years, there will still be about 13.5% of the reef remaining.

27 Examine the 2017 US Census Bureau data table and graph about how US commuters over the age of 18 traveled to work. Based on these data, what conclusions can be made about commuters in Texas as compared with commuters from all of the United States?

PARTIAL .25/1 - About 75% of people in the United States drove alone to work. NOT - More workers in Texas carpool than in the rest of the United States.

40. Emma plans a survey study to answer the question, "How do students spend their free time on weekends?" What questions will best allow her to collect quantitative data?

PARTIAL .67/1 - How many hours do you spend reading? - How many hours do you spend shopping?

4. Which situations are best modeled by exponential growth or decay?

PARTIAL .75/1 - the population of an invasive species that reproduces at a rate of 20% each year NOT - the position of a rocket when its velocity is increased by 90 meters per second. - the amount Carbon-14 a fossil has over time given the half-life of Carbon-14 is 5730 years

10. The architect uses a 30-60-90 right triangle to estimate the total length of the walkway. She measures the shortest side of the triangle as 15 meters. What are the lengths of the other two sides?

Side h = 30.0 meters side b = 25.98 meters

16. Examine the art image. Which statement best describes the patterns in this image?

Sine waves that are dilated and then translated.

1. An advertisement for a car manufacturer claims that the company's new cars have a higher fuel efficiency than their competitors. The advertisement used the following statistics based on a research study the car manufacturer did. How can the data be used to defend or reject the advertisement's claim?

The claim is false, because the mean mpg of the new cars is less than the mean mpg of the competitors' cars.

9. Rochelle builds a linear regression to help her estimate her monthly entertainment spending based on the number of hours she works each week. Let y be the amount of money she spends on entertainment, and let xx be the number of hours she works each week. She develops a regression that states that y=500−3.975x. The regression has an r2 of 0.9867. What can be stated about the correlation between Rochelle's monthly entertainment spending and the number of hours she works each week?

The data have a strong negative correlation.

2. An advertisement states that the following graph clearly shows a new model of car's life expectancy has increased by 9 times because the bar for the new car's median life expectancy appears to be 9 times greater than the bar for the old car's mean life expectancy. What is the statistical error in the graph?

The graph is cut off, so the life expectancy did not increase as suggested.

3. An advertisement displays the following graph and states that the average price of a competitor's new stock of computers has increased 5 times. What is the statistical error in the graph?

The graph is truncated, and the price of the computer did not increase as suggested.

4. Political scientists conduct a survey of 10,000 city residents to determine city bus use frequency. The following table shows the results. An advertisement cites the political scientists' work and states that since 66.55% of city residents do not ride the bus every day, voters need to approve a proposal to decrease the price so that more residents will ride the bus. What data might another political scientist use to reject this claim?

The other political scientist might state that more than 75% of city residents ride the bus at least once per week.

3. Examine the painting. Which statement best describes the patterns used to create this painting?

The painter used repeated and translated sine-like waves that merge and are reflected over a vertical line of symmetry.

35. Examine the graph of maximum land speeds. In 2018, Usain Bolt was arguably the fastest man in the world. A marketing agency promoted the safety of African safaris with the claim that Usain Bolt can run 3 times as fast as a hippo. What is the misleading information on this graph that led to that claim?

The scale starts at 25.

1. A marketing company takes a public opinion poll about the approval of a president from 10,000 randomly selected people in the Midwest. The poll determines that 75% of people surveyed believe the president is doing a good job. A political advertisement uses the data to state that 75% of Americans believe the president is doing a good job. This is an example of what type of bias?

area bias

29. A professor allows students to choose which measure of central tendency they want as their final course grade. Suppose a student has the following scores for the term: 90%, 92%, 84%, 76%, 92%, 86%, and 98%. What is the mean, median, and mode, and what is the best option to use as the final grade? All grades have equal weight.

best option = mode mode = 92% median = 90% mean = 88%

20. Examine the sound waves of a musical chord shown in the graph. Which statement best describes what is modeled by the graph?

periodic pattern using translations

19. Examine the image of an excerpt from a musical score. What geometric transformation describes this excerpt?

reflection

17. The photograph shows the Rainbow Bridge in Taipei, Taiwan. Parallel cables connect the bridge arch to the bridge deck as shown. Which geometric transformations are represented by the cables?

translation and dilation

6. Examine the graph The motion of a drone is modeled as velocity over time. What is the equation for this model?

v=2t^2−3t−4

1. A psychologist wants to construct a linear regression to predict how the number of occurrences of ADHD cases in a city is influenced by the number of public swimming pools in the city. The following data set shows the data the psychologist compiled. Let y be the number of ADHD cases in a city and x be the number of public swimming pools in the city. What is the linear regression that predicts this data set?

y=123,158.1786−12,574.1071x

2. A sociologist wants to construct an exponential regression to predict how the number of game shows on a television station affects the station's daily viewership. The following data set shows the data the sociologist compiled. Let y be the daily viewership of the television station and x be the number of game shows on the station. What is the exponential regression that predicts this data set?

y=354,767.7969e0.12x

1. A veterinarian uses a spring scale to weigh a cat. He records the cat's weight as 2 kilograms and notices the spring stretches 4 centimeters. Which expression represents the spring constant?

−19.6 N/4

7. An engineer draws an assembled gear in perspective. How does this gear appear when viewed from above?

(small white round, large gray round, teeth)

7. A historian builds a linear regression for the population of an ancient city based on the following data. The historian wants to predict the city's population based on the number of years following a major volcanic eruption. What information about the regression is accurate?

- The y-intercept is 87,315.7222. - y=5569.0333x+87,315.7222

25. A behavioral psychologist plans a true or false experimental study with toddlers. Which statements about this experiment must be true to use a binomial model?

- There are only 2 possible outcomes. - The number of trials is fixed in advance. - Each trial is independent.

3. Metropolis has a 200,000 population. In a poll of 200 Metropolis residents, 50 indicated a preference for temperate weather. What is the estimated population mean of the people who prefer temperate weather?

.25

4. A local high school's athletic department wants to calculate the proportion of students who have attended a girls softball game at the school. Using student email addresses, the department randomly chooses 250 students and emails them the question. Of the 150 who respond, 22 answer they have attended a girls softball game. What is the best estimate of the population proportion of students who have attended a girls softball game at the school?

0.147

2. A marketing firm wants to know how many people in District 6 have tried Popeyes' and Chick-fil-A's chicken sandwiches. Of the 10,000 people in District 6, 1500 are vegetarians or vegans and have never tried either sandwich, 5000 have tried both, and the rest have tried one or the other. What is the population proportion for people who have tried both sandwiches?

0.50

6. The following graph shows a scatterplot. A statistician believes that the correlation coefficient could be either 0.95, 0.61, −0.61, or −0.95. What is the correlation coefficient that best fits the graph?

0.61

2. A software company's advertisement claims that the number of glitches in its operating system has dramatically decreased over the first 9 months. The ad claims that 7 months after the software was released, the number of glitches had decreased by 300. The following graph shows the decrease in glitches over time. What is the actual decrease in glitches over the first 9 months?

100

23. A researcher is studying fraternal triplets who have developed from individual eggs. She knows there is an equally likely probability of each triplet being either sex. What is the probability that all three babies are boys?

12.5%

10. A psychologist conducts a survey about the number of days per year a person was happy compared to the number of rainy days that occurred in their city. Let y be the number of days per year the person felt happy, and let x be the number of rainy days that occurred in their city. The regression equation from the study is y=12+0.8643x. If there were 150 rainy days in a city, how many days would a person be predicted to feel happy?

141.65

15. A piece of music with a tempo of 100 beats per minute (bpm) has a playing time of 3 minutes. The piece is edited to have a playing time of 120 beats per minute. How long will the edited piece play in minutes?

2.5 minutes

13. A biologist on a 50-meter observation tower at the edge of a beach sees a great white shark swimming near the surface. The biologist sees the shark at an angle of depression of 10∘. How far is the shark from the observation tower?

283.56 m

1. A randomized telephone survey of adults in the United States determines that a certain number out of 504 respondents have one or more pets. They use p^ to construct a 95% confidence interval to estimate the proportion pp of American adults who have pets to be (0.56137,0.60529). How many respondents said they have one or more pets?

294

9. An architect designs a building with glass on all sides, solar panels on the roof, and an underground garage. To determine the amount of glass required, the architect creates this scale model. What amount of glass, in square meters (m2), is needed for the building?

37,440 m2

3. 6 liters of a gas has a pressure of 4 atmospheres. The gas's original pressure was 6 atmospheres. What was the original volume in liters?

4

5. Gold (Au) has a synthetic isotope that is relatively unstable. After 25.5 minutes, a 128-gram sample has decayed to 2 g. What is the half-life of this isotope?

4.25 minutes

11. A civil engineer plans to build an incline bridge over a river as shown. The bridge will span a section that is 35 meters wide, with ends of the bridge set back 2.5 m from each river bank. The engineer must apply right angle relationships because one river bank is 9 m higher than the other. What is the final length of this bridge?

41 m

3. A political scientist wants to predict how a city's population influences the number of voters who approved a clean air proposal. Let x be the city population and y be the number of voters who approved the proposal. The regression for the number of voters who approved the proposal is y=35,178+0.0614⋅x.If the city population was 325,000, how many voters approved the clean air proposal?

55,133

21. A sociologist designs a 10-item survey. Each item asks for an opinion on a scale of 1 to 5. How many different ways could a person answer the survey?

5^10

2. A tow truck accelerates at a rate of 0.5 meters per second when towing a car with a mass of 1200 kilograms

600 N

12. High-definition (HD) televisions today have a 16:9 aspect ratio (width to height). The advertised screen size is equal to the screen diagonal. Allowing for 22 inches of Styrofoam padding on all sides of the TV, what is the smallest possible length and width of a shipping box for a 75-inch HD TV?

68 by 40

22. A candidate for office plans to visit 6 cities before the state primary. How many different ways can the campaign staff arrange her travel route?

720

Final Exam (40 questions)

89.93%

36. The following advertisement popped up during an online search. What data is misused in the marketing claims?

= Lose 5% of your weight every week.

2. An arborist monitors growth of a baobab tree in an arboretum by standing 8 meters from the base of the tree and measuring the angle of elevation to the top. The angle of elevation to one tree is 30∘.

??

8. An economist wants to construct an exponential regression to predict the economic gross domestic product of a developing country. The following data set shows the data that the economist complied. What is the country's estimated gross domestic product in 10 years?

??

1. When looking at a graph of a variable that is normally distributed, what characteristic is necessary?

A normal distribution is symmetrical with a vertical line through its maximum value.

38. A company announces its profits to shareholders on a semiannual basis, as shown in the graph. Based on this regression model, what profit can shareholders expect in year 16?

About $110$110 million

32. An experimental study was designed to test the effect of noise on spatial reasoning among 10-year-olds. Each subject was given the same jigsaw puzzle in a quiet room. A month later, the same subjects were given the same puzzle with a TV playing cartoons and street noise. The researcher compared how long it took each subject to solve the puzzle in the two situations.

Dependent variable = time to solve puzzle Controlled variables = puzzle and age of children Independent variable = noise

3. An experiment was done to see if computer games were better at helping children learn multiplication facts than the traditional paper-and-pencil drills used in the classroom. Students in four third-grade classes were randomly selected to participate. The students in the sample population practiced their multiplication facts using a computer program, while the rest of the students did paper-and-pencil drills for the first semester of the school year. The same pre- and post-test was given to all students. Identify the dependent and independent variables in this experiment.

Dependent-success at learning multiplication facts; Independent-use of computer program to practice multiplication facts

31. Which research question is best suited for an observational study?

Do pedestrians jaywalk or use crosswalks when it is not rush hour?

6. Researchers have convened at a state hospital to observe 500 people with and without an iron deficiency. Which research question is best suited for an observational study of these people?

Do the people with an iron deficiency sleep longer than the people without an iron deficiency?

24. The table below from the American Red Cross shows the distribution of blood types in the United States. A local hospital holds a blood drive. By the end of the first day, 200 volunteers had donated blood. 60% of the units collected were type O and 25% were type A. How did the calculated probability compare to the empirical results?

Expected type O = 90 units Actual type O = 120 units Expected type A = 80 units Actual type A = 50 units

39. Which question meets the criteria of being both meaningful and suitable for a student to use for a research study?

Is there a correlation between class size and median grade in high school English classes?

8. An experimental study was conducted observing a 175-pound person exercising on a treadmill at a rate of 3 miles per hour. The data collected is shown in the graph. The values on the x-axis of the graph represent time exercised, and the values on the y-axis represent the number of calories burned. What does the graph reveal?

More time spent exercising on the treadmill resulted in more calories burned.

8. The Washington Monument is 169 meters tall with a square base 16.8 m wide. An artist plans to construct a replica on the shore of Lake Michigan in Wisconsin, using a scale factor of 1:8. What is the area of the replica's base in square meters rounded to two decimal places?

NOT 2.10

26. The quality control division evaluated reliability of a new cell phone model. In a random sampling of phones packaged and ready to ship to stores, the division found 28 did not turn on, 112 had minor software issues, and 735 had all desired functionality. What is a reasonable probability model for the quality of the cell phones that were sent to stores?

Will function as advertised = 84% Will require minor software fixes = 12.8% Will not turn on = 3.2%

33. According to the UNESCO Institute for Statistics, the global literacy rate among females is about 64%. What is this statistical measure called?

a population proportion

3. A marketing company takes an opinion poll of 100,000 college students. The poll asks: "Since you are a highly educated college student and are smarter than people who did not go to college, do you believe college graduates should earn more money than people who did not go to college?" What type of bias exists in this public opinion poll?

leading question bias

28. Examine the population data graph for the 50 US states. What values represent the median, interquartile range, and outliers?

median = 4,500,000 interquartile range = 2 millions to 7.5 million greatest outlier = 39,500,000 least outlier = 20,000,000

5. A marketing company surveys 10,000 emergency room doctors. The poll asks the doctors to choose which type of doctor they felt interacted with patients the best. The following data show the 10,000 emergency room doctors' opinions. What type of bias exists in this public opinion poll?

self-selection bias