algebra 2b - unit 6: statistics

many people who go to the beach are at risk of getting sunburn. to investigate how many take precautions to prevent sunburns, you approach 49 random people on the beach and ask them if they are wearing sunblock. of those surveyed, 38 of the 49 people said they are wearing sunblock. based on this information, what proportion of people who go to this beach wear sunblock?

.78

about what proportion of americans would you estimate like jazz music?

0.20 or 20%

what is the likelihood of the result, like the one the biologist observed in the study, occurring by chance?

1%

a grocery store owner found that 38% of a sample of 300 customers used coupons. he wants to be 95% confident in the potential range of the next 4,000 customers that use coupons. based on this information, what range of customers can he expect to use coupons?

1,300 to 1,740 customers

unit 6 exam

100%

you collect a sample of 10 randomly selected students from a local university and have them each take an iq (intelligence quotient) test. what would be your best estimate of the average iq of students at the university?

105

the average cost of dishwashers sold by an appliance company is $502 with a standard deviation of $84. assume that the company's dishwasher prices are normally distributed. you decide to purchase a dishwasher from this company for $400. what percentage of dishwashers sold by this company are sold for less than $400?

11%

approximately what percentage of the population has a z-score between 0.0 and 0.35?

13.68%

approximately what percentage of the population has a z-score between 1.0 and 3.25?

15.81%

the admissions committee at state college found that the student body had an average grade point average (gpa) of 2.8 with a standard deviation of 0.4. the gpa values were normally distributed. what percentage of students had gpa's outside the range of 2.4 to 3.6?

18.2%

a tech company develops a navigation app for smartphones that can compute the usual distance it takes to get from one location to another. the company collects location data from 100 smartphones to determine how long it takes to drive from cleveland, ohio, to detroit, michigan. what would this range be?

2.66 to 2.90 hours

a sample of 21 randomly selected students has a mean gpa of 3.11, with a standard deviation of 0.50. based on this information, create a 95% confidence interval for the mean gpa of all students.

2.89 to 3.33

a computer manufacturer estimates that 3% of the computers they produce will be returned for refunds, with a margin of error of 0.5%. if the manufacturer sells 8,000 computers, what is the expected range of computers that will be returned for refunds?

200 to 280 computers

janine and laura both took a standardized math test. the scores were normally distributed with a mean of 75 and a standard deviation of 11. janine earned a score of 76, whereas laura earned a score of 89. about what percentage of people had a score between janine's and laura's scores?

36%

devon expects the algorithm to offer approximately 5,000 movie recommendations this month, and he wants to calculate the number of recommendations that are expected to be "good." what would the likely range of "good" recommendations be?

4,200 to 4,500 good recommendations

what is the best estimate of state citizens, in general, that support the proposal?

4.1

a researcher is interested in understanding the annual salaries and gender of software engineers in california. she collects a random sample of software engineers from california and obtains the following data: based on the data, what are the best estimates of gender and income in the population? select all that apply.

43% of software engineers in california are women. the average software engineer in california earns $97,200 per year.

in a particular soccer league, the mean height of the players is 67 inches with a standard deviation of 3 inches. the heights are normally distributed, so 95.4% of the heights fall into a certain range of values around the mean. select the height(s) that fall(s) into this range of values. select all that apply.

62, 70, 72

all of the students in mr. clarke's class took a benchmark test. when mr. clarke analyzed the students' grades, he found that they were normally distributed and that __[blank]__ of the students received grades with z-scores between −0.75 and 1.15

64.83%

jason took his siberian husky dog to the veterinarian. the dog was put on a scale and found to weigh 52 lb. assume that the population mean weight of siberian huskies is 49 lb. with a standard deviation of 7. the weights of huskies are normally distributed. what is the approximate percentage of huskies that weigh less than jason's dog?

67%

all the houses in stanton county have a mean size of 1,650 square feet with a standard deviation of 320. assume the distribution of their size follows a normal distribution. if you inspected the houses in stanton county, about what percentage would be between 1,330 and 1,970 square feet?

68%

on a particular swimming team, the average time to swim a lap in a pool is 87 seconds with a standard deviation of 11. the swimming times are normally distributed, so 95% of the times fall into a certain range of values around the mean. select the times that falls into this range of values.

68, 81, 108

mr. conley analyzed his students' final exam scores and found that the students achieved a mean score of 85 with a standard deviation of 7. the scores were normally distributed, so 95% of the scores fell in a particular range of values around the mean. select the scores that fell into this range of values.

72, 84, 98

amanda scored 87% on a math test. the following curve shows the results of her whole class. about what percentage of students did amanda score higher than?

77.34%

what is the approximate probability that a randomly chosen observation falls within the shaded region, which is everything below one standard deviation above the mean?

84%

a particular group of miniature poodles has a mean weight of 13 kg with a standard deviation of 2 kg. the weights are normally distributed, so 95% of the weights fall into a certain range of values around the mean. select the weights that fall into this range of values.

9.5, 12, 16.5

what is the probability that a randomly chosen observation falls within the shaded region?

95%

which answers describe a data set that is not a normal distribution? select all that apply.

a data set that is asymmetrical a data set that has a mean of 15 and a median of 9 a data set where 50% of the data are more than 1 standard deviation from the mean

which scenario is explored most effectively by conducting an observational study?

a marine biologist wants to study the feeding behavior of sharks in their natural habitat. she wants to gather data without influencing the shark's natural behavior.

which of the following results would indicate a statistically significant effect in a study?

an observed result is less than 2% likely to occur by chance.

antoine is a ceo who wants to get people to invest in his company. at a meeting with potential investors, he shows them two figures that display how successful his company is compared to the rival competing company. each figure shows company revenue by year since 2001: how might antoine be misleading potential investors?

antoine could be cherry-picking data by excluding company revenue from 2016 and beyond. the y-axis of revenue for the competing company starts at 1 million dollars, rather than zero, making it look like the competing company is not earning as much revenue as antoine's company. the y-axis of revenue for the competing company ends at 88 million dollars, whereas the y-axis for antoine's company ends at 3.5 million dollars. this makes the bars of the competing company's revenue shorter.

antonia likes to play chess as a hobby. to get an advantage over her potential chess opponents, she decides to run a stimulation to see the most common opening moves in a game of chess. she sets her chess computer program to play 100 first moves in the game of chess. antonia concludes that of the 20 possible opening moves in chess, most players will move the pawn piece in front of the queen forward two spaces. what are some potential problems with antonia's simulation and her conclusion?

antonia used a small number of simulations antonia assumes that people think and behave like her chess program. in reality, people might behave differently than a chess computer

a university gives a math placement exam to all incoming freshmen. the university changes the exam each year after analyzing it to help ensure that the scores are consistent for each freshman class. the test scores are normally distributed with an average score of 72% and a standard deviation of 4%. which statements are justified based on the data?

approximately 68% of the students score between 68% and 76%. approximately 95% of the students score between 64% and 80%. approximately 99.7% of the students score between 60% and 84%.

a scientist compares the body lengths between three samples of species of salmon: chum salmon, pink salmon, and atlantic salmon. to do this, he collects six fish of each species and measures their lengths. the body lengths from the three samples of salmon are below, in cm: based on this data, which of the following are true? select all that apply.

atlantic salmon have the highest length, on average. chum salmon are the shortest in length, on average. the average length of pink salmon is between chum salmon and atlantic salmon.

a farmer estimates that 4% of the 1,400 fruit trees on his farm will fail to produce fruit, with a margin of error of 2.5%. based on this information, which statements are true?

between 21 and 91 trees can be expected to fail to produce fruit. because there is a margin of error of 2.5%, between 1.5% and 6.5% of the fruit trees will fail to produce fruit. the farmer should calculate 1.5% of 1,400 and 6.5% of 1,400 to find the range of trees that will fail to produce fruit.

the annual springfield marathon takes an average of 4.8 hours to complete with a standard deviation of 0.8 hours. the completion times are normally distributed. for each runner, find the approximate percentage of runners who completed the marathon in less time.

bill completed the race in 3.6 hours : 7% maureen completed the race in 4.2 hours : 23% jason completed the race in 5.5 hours : 81%

a business manager asks his employees how satisfied they are with their jobs using an anonymous survey every month. high numbers indicate greater job satisfaction, whereas low numbers indicate dissatisfaction. if you use medians to compare the data, which is true about the employee satisfaction?

both months had equal employee satisfaction.

lesson 26

data from surveys

a psychologist randomly assigns people to listen to either rock music or classical music to see if listening to a particular type of music affects mood. the participants then fill out a questionnaire to assess their mood on a scale from 1 to 10. the psychologist finds that participants who listened to rock music had an average score of 1.6 points higher in mood than those who listened to classical music. he simulates the results of this study by randomly assigning the values to different groups 150 times. he finds that 36 of the simulated outcomes show mood differences between groups that are 1.6 points or greater. what should the psychologist conclude?

his results are not statistically significant. therefore, there is no effect of music on mood in this study.

all these figures show data on the number of units sold for the top 5 best-selling music artists. the artists and the approximate number of units they sold are the beatles (281 million), elvis presley (227 million), michael jackson (234 million), elton john (193 million), and madonna (174 million). based on what you have learned about misleading figures, which of the following figures is the least misleading?

https://cdstools.flipswitch.com/asset/media/1240222

researchers are testing a vaccine for a particular virus. study participants are vaccinated and observed for 24 weeks. at the end of the study, the researchers conclude with 95% confidence that the vaccine is 94% effective, with a margin of error of 0.3%. which of the following statements are true?

if the study were repeated several times, 95% of the studies would find the vaccine between 93.7% and 94.3% effective. the margin of error in this study is relatively low, which means that the statistic calculated by the researchers is very similar to the true parameter.

a university conducts a study of tobacco use among 1,000 of its students. the school surveys male and female volunteers to find the frequency of tobacco use. the study finds that, of the people surveyed, 250 men and 50 women regularly use tobacco. the university concludes that male students use tobacco more frequently than female students. which of the following situations would create a confounding variable (lurking variable) that could impact the study?

if the university surveyed more men than women, the number of male and female participants would be a confounding variable. if the men who took the survey all used tobacco at least once in high school, the participant history could be a confounding variable.

suppose the average height of men in the united states is estimated to be 175 cm. based on this data, which statement is true?

men who play basketball at ssu are shorter than the average american man

muriel is conducting research for a study about the work habits of employees in an office. she collects data by interviewing employees out of a total of 40 employees that work in the office. what sampling method would provide her the most representative sample?

muriel writes down the names of all 40 employees on individual pieces of paper. she then folds the pieces of paper up, places them in a bowl, and shakes the bowl around to mix up the pieces of paper. she then draws 10 pieces of paper out of the bowl and interviews the employees that have their names on those tickets.

lesson 27

normal distributions

julie is an education researcher interested in understanding the effects of tutoring on student performance. there are many ways she could study this question. match each research method with a description of how julie could conduct this study.

observational study : without interacting with any students, julie randomly selects 20 students from a tutoring program and 20 students not a tutoring program. she then looks up their grades in the student records. experiment : julie randomly assigns a sample of students to receive tutoring assistance or a control condition where they do not receive tutoring. she then examines changes in student grades at the beginning of the study vs. three months later survey : julie sends out a questionnaire to ask students whether they have used a tutor. the questionnaire also asks students to rate how they are doing in school on a scale from 1 (not very well) to 10 (very well)

an educational administrator wants to test if students randomly assigned to a mentorship program perform better in english classes than students who were assigned to a different educational support program. she conducts a study between these two groups and finds that students in the mentorship program had test scores 5 points higher than those assigned to a different program, on average. she conducts 200 simulations of the results, assuming no differences in scores between the groups. which of the following would suggest that the mentorship program was effective at improving student performance?

of the 200 simulations, 2 showed differences of 5 points or greater between groups. of the 200 simulations, 9 showed differences of 4 points or greater between groups.

the chart shows unemployment rates for us states in the new england and pacific regions from april 2020. which of the following statements is true based on comparing the means?

pacific states had a greater unemployment rate than new england states.

based on this information, raymond predicts that he will be more likely to draw a spades suit from a deck of cards rather than a club suit. what is wrong with this prediction?

raymond ran a low number of simulations. therefore, the predictions of the simulation could vary considerably from the actual results.

an elementary school principal wants to see if upgrading classroom technology will improve student learning. she upgrades the technology in all third and fourth grade classrooms but does not upgrade the technology in other grade-level classrooms. she finds that the students who received the technology upgrades did not perform any better than students who did not receive the upgrades. based on this, she decides not to upgrade any more school technology. what is the flaw in her reasoning?

she cannot be sure her results are due to the technology or differences in student grade level

lesson 28

simulations

the gpa results of two groups of students from gerald fitzpatrick high school and springfield high school were randomly sampled: based on this data, which high school has higher-performing students?

springfield high school

lesson 25

statistical studies

jason works in human resources at a financial company. he wishes to investigate whether employees are happier working in the company office in cleveland than in the company office in new york city. to do this, he follows the standard steps of statistics, as discussed in the lesson. match each step in the process with the correct description.

step 1 : jason decides he needs to investigate the question: "are company employees working in cleveland happier than those working in new york city?" step 2 : jason sends a survey to a random sample of employees in cleveland and a random sample of employees in new york city step 3 : jason analyzes the data to compare the happiness of cleveland employees to the happiness of new york employees. he finds that the sample of employees in cleveland, on average are happier than the sample of employees in new york city step 4 : jason concludes that cleveland employees are happier than new york city employees

laura is interested in investigating whether a tutoring program will improve students' grades. to do this, she follows the standard steps of using statistics. match each step in the process with the correct description.

step 1 : laura decides she will investigate the question, "does tutoring improve students' grades?" step 2 : laura randomly assigns students to a tutoring program or a control condition. she then collects information on their grades when the program is finished. step 3 : laura analyzes her data and finds that students in the tutoring program have higher grades than students who were not in the tutoring program. step 4 : laura concludes that the tutoring program is effective at improving the grades of students.

an economist wishes to model potential outcomes in the stock market in the upcoming year. to do this, she decides to conduct a simulation study. what would be the best way to go about doing this?

the economist conducts a model with 10,000 simulations of the stock market, basing her simulations on stock market data from the past 5 years.

a camera manufacturer sends out 90 camera shipments each week, and each shipment contains 1,000 cameras. an inspector inspects 2 of the shipments before they are sent. after the inspections, the inspector concludes with 98% confidence that 0.9% of each shipment will be defective, with a margin of error of 0.5%. what conclusion can you draw from the size of the margin of error in this inspection?

the margin of error in this inspection is relatively low. this means that for 98% of all shipments, the statistic calculated by the inspector, 0.9%, is very similar to the true parameter.

an automobile engineer calculates the average fuel efficiency for a specific make of cars. the cars have a median fuel efficiency of 31 miles per gallon (mpg) with a standard deviation of 3 mpg. he is not sure if the data are normally distributed. what would be signs that the data are normally distributed?

the mean fuel efficiency is about 31 mpg. 95% of the fuel efficiency measurements are between 25 and 37 mpg.

a pumpkin farmer collects 20 pumpkins randomly sampled from his pumpkin patch and weighs them. the mean weight of the pumpkins is 26 lb. he wonders whether the weight of his pumpkins follows a normal distribution. which answers are clear signs that the pumpkin weights are not normally distributed?

the median pumpkin weight is 10 lb the median pumpkin weight is 35 lb 75% of pumpkins in the sample have weights higher than the mean

a pollster reports that 61% of voters plan to vote for ralph thoreau for state senator. the pollster indicates that the margin of error for this report is 7%, with a confidence level of 85%. what is the most effective way for the pollster to reduce this margin of error?

the pollster should poll more people

a pollster wishes to simulate how people will vote in the upcoming state election. based on poll data gathered by random people in the state, she simulates the outcomes of the election 10,000 times and determines that candidate marcy morino has a 72% chance of winning the vote to be state governor. based on this, she concludes the winning candidate will likely be marcy morino. however, the other candidate, joseph ramirez, won the election. which of the following would likely be the biggest problem with the pollster's conclusion?

the pollster's surveys were not representative of the voter population. the sample population was random people in the state, not likely voters in the state. the population represented by the sample in the survey did not show up to vote for marcy morino.

a researcher is interested in determining the effects of social media use on loneliness. she conducts a correlational study where she measures the amount of time people spend on social media. the 400 participants in the study also report how lonely they feel on a 1 (not at all lonely) to 10 (very lonely) scale. she finds that the more time people spend on social media, the lonelier they feel. she concludes that social media is causing people to be lonely. identify the flaw with the researcher's study and conclusions.

the researcher concludes with a cause and effect relationship from her data.

smallmouth bass is a species of freshwater fish native to the areas around the mississippi river, the hudson bay basin, and the great lakes. a researcher at the university of michigan is interested in studying the health of smallmouth bass in lakes throughout the united states. he catches 30 smallmouth bass out of lake huron (one of the five great lakes surrounding michigan) and measures how healthy they are. he concludes that smallmouth bass in the us are relatively healthy, on average. what is the problem with this study and the researcher's conclusion?

the researcher did not randomly sample from all the available sources of smallmouth bass. because of this, the assessment of smallmouth bass health may not generalize to the entire population.

a political campaign researcher sends a survey out to 100 randomly selected voters in massachusetts. the survey asks the voters how they plan to vote on a proposal to raise taxes on casinos. the voters respond to one of the three options: voting for the proposal, voting against the proposal, or if they are undecided. the researcher finds that 54% of the voters plan to vote for the proposal, 40% plan to vote against the proposal, and 6% are undecided. what option is most likely the purpose of this study?

the researcher wants to get an estimate of how many voters in massachusetts will vote for and against the proposal.

a food lab tests the sugar content in one serving of joanna's oat cereal. the lab concludes with 90% confidence that each serving contains 8 grams of sugar. the lab states that the margin of error for this study is 4.2 grams of sugar. based on the margin of error, did the lab deliver meaningful results?

the results are a poor representation of the true parameter. the margin of error is relatively large, and the confidence is relatively low.

what is the correct conclusion that the botanist should make?

the results are not statistically significant. they do not suggest that the pH level of the soil had any effect on foxglove plant growth.

a researcher wanted to investigate how frequent diabetes was in elderly adults. he surveyed 100 elderly adults at nursing homes in the region to see how many of them had diabetes. he finds that 13 of the respondents have diabetes and publishes a report claiming that 13% of elderly adults have diabetes. what is the major problem with the researcher's investigation and report?

the sample of elderly adults at nursing homes is not likely a representative one. therefore, 13% might not reflect the frequency of diabetes in the elderly population.

a botanist wants to examine the effects of a chemical on plant growth, so he runs an experiment. he gives the chemical to one species of plant on the left side of his greenhouse. the other species of plant on the right side of the greenhouse is assigned to the control group and does not receive the chemical. the botanist discovers that the plants that received the chemical grew more, on average, than those that did not receive the chemical. he concludes that the chemical is effective for promoting plant growth. what are the problems with this experiment and the reasoning of the botanist?

the side of the greenhouse the plants are on and the plant species are confounding variables. it is difficult for the botanist to rule out other explanations for the results that do not involve the chemical. the botanist failed to randomly assign the plants to each condition. this makes it difficult to know if the chemical actually caused plants to grow.

evan conducts an experiment on rats to investigate if a drug will change how much they sleep. he randomly assigns 20 rats to receive the drug and 20 rats to receive a placebo in a controlled laboratory environment. he then records how much the rats sleep over a week. Rats receiving the drug slept significantly less than those receiving the placebo. evan concludes that the drug causes a decrease in how much sleep occurs in rats. what is the problem with evan's conclusion?

there are no apparent problems. if evan randomly assigned the rats to receive the drug and placebo, this helps eliminate the possibility that other factors than the drug influenced the rats' sleep.

is there enough evidence that fuel a is better than fuel b? why?

there is not enough evidence that fuel a is better than fuel b. the effect of fuel type on fuel efficiency is not significant.