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Name the Inference
| Scenario | Inference Procedure |
|---|---|
| Estimate the length of time that it takes the average letter sent locally to arrive at its destination and state the margin of error. 92 letters were sent to various local addresses. | Confidence Interval for a Population Mean |
| Estimate the length of time that it takes average first graders to tie their shoes and state the margin of error. 1008 first graders were surveyed. | Confidence Interval for a Population Mean |
| What is the average loss for new businesses during their first year? 82 new businesses were tracked. | Confidence Interval for a Population Mean |
| A police chief is interested in estimating the average amount of money that is stolen during a bank robbery. She investigates 42 recent bank robberies. | Confidence Interval for a Population Mean |
| The school average on the statistics final is 78%. 45 students are assigned a computer supplement. Estimate the average score on the final for students who were assigned the supplement. | Confidence Interval for a Population Mean |
| Estimate the average number of pinecones that a 30-year-old pine tree produces each year and state the margin of error. Fifty-five pine trees were observed over a one-year period. | Confidence Interval for a Population Mean |
| A new surgery technique boasts a small incision size. The technique was used on 90 patients. Estimate the mean incision size. | Confidence Interval for a Population Mean |
| What is the average voter turnout during an election? 38 cities reported their voter turnout during the last election. | Confidence Interval for a Population Mean |
| What is the percent fat content of the average American female? 2,000 women were tested. Cite the margin of error. | Confidence Interval for a Population Mean |
| You want to estimate the average number of texts that college students send each day. You survey 150 college students. | Confidence Interval for a Population Mean |
| How likely are people to agree to answer a phone questioner when a market researcher calls? A market researcher called 150 people and wrote down the results. | Confidence Interval for a Proportion |
| How much more likely is it that a pine nut planted in fertilized soil will germinate compared to pine nuts in nature? Biologists know that 12% of all pine nuts in nature will germinate. 55 pine nuts were planted in fertilized soil. | Confidence Interval for a Proportion |
| You have conducted a survey about whether Americans are in favor of additional nuclear power plants being constructed.Determine a likely range of values for the true percent of Americans in favor of the proposition. | Confidence Interval for a Proportion |
| What is the president's approval rating? 1500 US citizens were asked whether they approved of the job that the president was doing. | Confidence Interval for a Proportion |
| What proportion of all business owners inherited the business from their parents? 500 business owners were surveyed. | Confidence Interval for a Proportion |
| A new treatment is being tested to see how much more effective it is in curing people with the Ebola virus. The old treatment has a 34% success rate. 55 people infected with Ebola were given the new treatment. | Confidence Interval for a Proportion |
| What proportion of car accidents cause serious injuries? 2500 accidents were studied. | Confidence Interval for a Proportion |
| About what percent of college students own a car? 700 college students were surveyed. | Confidence Interval for a Proportion |
| How often do first dates end with a kiss? 85 first dates were observed. | Confidence Interval for a Proportion |
| The music industry is interested in estimating the percentage of all music played that has been legally purchased. They investigate 500 randomly selected songs on people’s music players. | Confidence Interval for a Proportion |
| How much more effective against insects are plants with an insect resistant gene than plants without this gene? 500 plants with the gene and 500 plants without the gene were measured for the number of insects per plant. | Confidence Interval for the Difference Between 2 Means |
| How much more money do students have to spend on private universities compared with public universities? Costs of forty private universities and forty public universities were researched. | Confidence Interval for the Difference Between 2 Means |
| How much faster can sober drivers react compared to inebriated drivers? 400 sober drivers and 300 inebriated drivers were tested. | Confidence Interval for the Difference Between 2 Means |
| How much larger is the average bail that is set for male defendants than for female defendants? 55 male defendants and 35 female defendants were studied. | Confidence Interval for the Difference Between 2 Means |
| How much more time do high school students spend watching television than college students? 75 college students and 75 high school students were asked what percent of their free time is spent watching television. | Confidence Interval for the Difference Between 2 Means |
| How much more gasoline do boaters use in Lake Tahoe compared to Fallen Leaf Lake? 85 boats in Lake Tahoe and 35 boats in Fallen Leaf Lake were researched. | Confidence Interval for the Difference Between 2 Means |
| How much higher is the suicide rate in New York on gloomy days compared to sunny days? The number of New York suicides that occurred during each of 35 gloomy days and the number that occurred during each of 55 sunny days were collected. | Confidence Interval for the Difference Between 2 Means |
| A study was done to determine how much faster the average fast food restaurant serves customers vs. the service time of sit down restaurants. 90 fast food restaurants and 80 sit down restaurants were observed. | Confidence Interval for the Difference Between 2 Means |
| How much more traffic is there on Friday afternoon compared with Saturday afternoon? The number of cars was tracked on 40 randomly selected Fridays and 40 randomly selected Saturdays. | Confidence Interval for the Difference Between 2 Means |
| You are interested in determining by how much the technology stocks have outperformed financial stocks in the previous quarter. You research price changes of 35 technology stocks and 40 financial stocks. | Confidence Interval for the Difference Between 2 Means |
| How much better do older siblings do than younger siblings in high school? GPA records of 80 two-child families were looked at. | Confidence Interval for Paired Data |
| How many more calories do people consume on days that they exercise vs. days without exercise? Caloric intake of 600 participants was charted for a day when they did exercise and a day when they did not exercise. | Confidence Interval for Paired Data |
| How many more people ride the gondola on Saturdays compared to Sundays? Saturday and Sunday counts were tallied for 15 randomly selected weekends. | Confidence Interval for Paired Data |
| How much does proper lighting improve museums? Visitors were asked to rate the museum on a scale from 1 to 10 both before new lighting was installed and after the new lighting was installed. | Confidence Interval for Paired Data |
| How much does exercise lower blood pressure? 100 people took part in a survey where they were tested before and after an extensive exercise program. | Confidence Interval for Paired Data |
| How much better has the NASDAQ done than the Dow Jones industrial this year? The daily point gains and losses have been charted since January 2. | Confidence Interval for Paired Data |
| 85 people were observed to see how many seconds they spend brushing their teeth and how many seconds they spend brushing their hair. Estimate the average difference. | Confidence Interval for Paired Data |
| 45 students were asked how many hours they spend per week enjoying outdoor entertainment and how many hours they spend per week enjoying indoor entertainment. Estimate the mean difference between the average outdoor and indoor entertainment per week. | Confidence Interval for Paired Data |
| How many more minutes do students spend doing math homework compared to attending class? 46 math students were asked how many minutes they spent last week in class and how many minutes they spent doing their homework. | Confidence Interval for Paired Data |
| How much does a speed reading course help? Words per minute read was charted before and after the course for 80 students. | Confidence Interval for Paired Data |
| How much more likely is it that a startup restaurant will last for at least a year when it is part of a larger chain compared to one that is a non-chain restaurant? 100 startup chain restaurants & 80 startup non-chain restaurants were observed for a year. | Confidence Interval for the Difference Between 2 Proportions |
| How much more likely are college teens than non-college teens to drink alcohol? 90 college teens and 90 non-college teens were asked if they had an alcoholic beverage last weekend. | Confidence Interval for the Difference Between 2 Proportions |
| What is the difference in the pass rate for statistics students who purchase the textbook vs. students who purchase the e-text? 700 of each were observed. | Confidence Interval for the Difference Between 2 Proportions |
| What is the difference between political affiliation before and after a war? 2500 citizens were asked if they were republicans both before and after the war. | Confidence Interval for the Difference Between 2 Proportions |
| How much more often do women order dessert compared to men? 85 men and 73 women at a restaurant were observed to see if they ordered dessert. | Confidence Interval for the Difference Between 2 Proportions |
| How much more likely is it for a person to own a dog than a cat? 100 people were asked whether they own a dog and whether they own a cat. | Confidence Interval for the Difference Between 2 Proportions |
| How effective are instant store coupons in getting customers to purchase an item? 500 customers were observed when the instant store coupon was available and 400 were observed when it was not available. | Confidence Interval for the Difference Between 2 Proportions |
| How much more likely is it for a store to be closed on the fourth of July vs. Memorial Day? 2,000 stores were observed. | Confidence Interval for the Difference Between 2 Proportions |
| How much greater is the proportion of senior citizens that attend a play at least once per year compared with attendance for people in their twenties? 100 senior citizens and 100 people in their twenties were questioned. | Confidence Interval for the Difference Between 2 Proportions |
| A medical researcher tracked 10,000 nonsmokers and 9,000 smokers over the next five years in order to estimate how much more likely smokers are to die compared with nonsmokers. | Confidence Interval for the Difference Between 2 Proportions |
| How long can you expect to live if your cholesterol level is 230? Data has been taken from 45,000 people with varying levels of cholesterol. | Prediction for a Single Value of y for a Fixed x |
| 100 students were asked how many hours they studied for their final exam and what percent they received on the exam. Estimate the average score that students get who spend 8 hours studying for the final exam. Cite the margin of error. | Prediction for a Single Value of y for a Fixed x |
| A criminal justice professor researched crime numbers for 2000 areas of varying population density. Estimate the number of crimes committed per year in a town with a population density of 5000 people per square mile. | Prediction for a Single Value of y for a Fixed x |
| 300 people of differing ages were asked how old they were and how much money they spent on clothes. Come up with an estimate and margin of error for the amount of money the average 42 year old spends on clothes. | Prediction for a Single Value of y for a Fixed x |
| 5000 people from all over the city were asked how far from the stadium they lived and how many sporting events they attend each year at the stadium. Estimate the average number of sporting events people attend who live 20 miles from the stadium. | Prediction for a Single Value of y for a Fixed x |
| 3000 married couples who had been married for various amounts of time were observed for one year to see how many times they fought. Estimate the mean number of fights for couples who have been married for five years. | Prediction for a Single Value of y for a Fixed x |
| 500 police officers with various numbers of years of experience were studied to see how long it took them to give a simple speeding ticket. Estimate the mean amount of time it takes officers with three years of experience to give a traffic ticket. | Prediction for a Single Value of y for a Fixed x |
| Is the average commute time to work the same for all counties in California? 4000 workers from all over California were asked what county they were born in and how long it took them to commute to work. The statewide average commute is 27 minutes. | Prediction for a Single Value of y for a Fixed x |
| A biologist counted the number of coyotes in 300 areas that had various amounts of rainfall per year. Estimate the number of coyotes in an area that has 22 inches of rainfall per year. | Prediction for a Single Value of y for a Fixed x |
| 75 people were questioned about their age and the amount they have already saved for retirement. Based on this data, can you provide a range of values that your 36 year old instructor has likely saved for retirement? | Prediction for a Single Value of y for a Fixed x |
| Last year the average hotel room at Stateline was $60 per night. A study was done to determine if the average cost per night for rooms this year has increased. What can be concluded? | Hypothesis Test for a Population Mean |
| Is the average age of the voting public greater than 40? Two thousand randomly selected voters were surveyed. | Hypothesis Test for a Population Mean |
| Do people spend on average fewer than 2 weeks per year on vacation? 1500 people were surveyed. | Hypothesis Test for a Population Mean |
| The average weight of women in their fifties is 135. You are interested in seeing if this average is different for women in their fifties who exercise daily. You weigh 71 women in their fifties who exercise daily. | Hypothesis Test for a Population Mean |
| The average cholesterol level for people in their forties is 192. You are interested in seeing if the average cholesterol level is different for vegetarians in their forties. 56 vegetarians in their forties were tested for cholesterol level. | Hypothesis Test for a Population Mean |
| The average SAT score for UCLA students is 1264. You are interested to see if the average SAT score is different for UCLA students who come from rural areas. 65 such students were asked what their SAT scores were. | Hypothesis Test for a Population Mean |
| Last year politicians averaged 2000 travel hours. This year, with an election occurring, it is expected that they will travel more hours. 34 politicians were tracked this year for their travel time. What can be concluded? | Hypothesis Test for a Population Mean |
| Over the past many years, the average daily attendance at the theatre was 147. This year forty randomly selected days produced a mean of 150. Has attendance improved this year? | Hypothesis Test for a Population Mean |
| Will a light bulb last for more than 500 hours on average? 200 bulbs were observed. | Hypothesis Test for a Population Mean |
| Typically, your shop has 140 customers per day. Over the last thirty days you have a special advertisement in the Daily Tribune. You chart your daily number of customers. Is this ad effective? | Hypothesis Test for a Population Mean |
| Do more than 70% of statistics students pass their course? 200 statistics students were observed. | Hypothesis Test for a Population Proportion |
| If there is not enough of one gender in the frog population, will more of that gender be born in the next generation? 3000 tadpoles were born to a frog community where there were a disproportionate number of female frogs. | Hypothesis Test for a Population Proportion |
| Do more than 99.9% of women who are given the vaccine stay free of ovarian cancer? 30,000 women were observed. | Hypothesis Test for a Population Proportion |
| A new vaccine for AIDS is currently being tested. If the vaccine is at least 80% effective, then the vaccine will be recommended for the African population. 2000 people were given the vaccine. | Hypothesis Test for a Population Proportion |
| Are more than 1/28 of all people born on the day of a full moon? 5000 randomly selected people were asked if they were born on the day of a full moon. | Hypothesis Test for a Population Proportion |
| Are blondes more likely to have a boyfriend than the rest of the single world? Currently 38% of all single women have a boyfriend. A random sample of 300 blondes was investigated. | Hypothesis Test for a Population Proportion |
| Does the home team win the majority of the time? 100 games were observed. | Hypothesis Test for a Population Proportion |
| Are the majority of community college students in college in order to better their careers? 75 college students were surveyed. | Hypothesis Test for a Population Proportion |
| Do more than 98% of people who are given the H1N1 vaccine stay free of the H1N1 flu? 2000 people were observed. | Hypothesis Test for a Population Proportion |
| 8% of all Americans experience a major medical problem in a given year. This year 900 vegetarians were tracked to see if fewer of them experienced a major medical problem. | Hypothesis Test for a Population Proportion |
| Do men spend a higher percent of their working hours in meetings than women? 75 men and 75 women were questioned. | Hypothesis Test for the Difference Between 2 Means |
| Are people who drink coffee more stressed than those who do not drink coffee? 300 coffee drinkers and 200 non-coffee drinkers were tested for stress level (on a 100 point scale). | Hypothesis Test for the Difference Between 2 Means |
| Is the recovery time from ACL surgery shorter for patients who have health insurance? 300 patients with health insurance and 200 patients without health insurance were studied for their recovery time after the ACL surgery. | Hypothesis Test for the Difference Between 2 Means |
| Do fatalities at a crime scene occur less often if there are more police officers involved? 45 crimes where only one officer was at the scene and 34 crimes where more than one officer was called were examined. | Hypothesis Test for the Difference Between 2 Means |
| Do families of students at private universities have higher incomes than those at public universities? 200 private university students and 300 public university students were surveyed. | Hypothesis Test for the Difference Between 2 Means |
| Do people who wear hats spend more money at the mall than people who do not wear hats? 300 of each were followed. | Hypothesis Test for the Difference Between 2 Means |
| Are African Americans taller than Caucasians? 10,000 African Americans and 10,000 Caucasians were measured. | Hypothesis Test for the Difference Between 2 Means |
| The police chief is interested in whether chases end faster when the officer is on a motorcycle vs. when the officer is in a car. 40 chases with a motorcycle and 40 chases with a car were observed. | Hypothesis Test for the Difference Between 2 Means |
| Do people living in houses make more money than those living in condos? 300 people living in houses and 200 living in condos were questioned. | Hypothesis Test for the Difference Between 2 Means |
| Will plants grow larger in artificially fertilized soil then in organic soil? 55 plants were grown in organic soil and 55 plants in artificially fertilized soil. | Hypothesis Test for the Difference Between 2 Means |
| Is there evidence to suggest that people spend more time watching TV than all other forms of entertainment combined? 70 people were asked about the hours they spent watching TV and the hours they spent on other forms of entertainment. | Hypothesis Test for Paired Data |
| Does the DMV’s driver’s course for speeders reduce speed? 200 people were clocked to for their average freeway speed before they took the course and after they took the course. | Hypothesis Test for Paired Data |
| Do people smoke less when the cigarettes cost more? 500 people were tracked before a 30% cigarette tax was imposed and after the tax was imposed. | Hypothesis Test for Paired Data |
| Eighty-five P.E. students were tested for bicep girth before and after taking a weightlifting class. Is there evidence to suggest that mean bicep girth increases after taking a weightlifting class? | Hypothesis Test for Paired Data |
| Are more crimes committed during the daylight hours compared to night? Police records from 200 consecutive days were considered. | Hypothesis Test for Paired Data |
| Do people spend more time listening to music in their cars than at home? 600 people were asked how many hours they listened at home and how many hours they listened in their cars. | Hypothesis Test for Paired Data |
| Do wives spend more time on household chores than their husbands? 50 wives and their 50 husbands were surveyed. | Hypothesis Test for Paired Data |
| Does election-spending reform truly curtail spending? Races in 50 counties throughout the US were studied before and after the passage of the election spending reform act. | Hypothesis Test for Paired Data |
| Are people happier after they get married? 100 people were asked on a scale from 1 to 10 how happy they were one year before marriage and one year after marriage. | Hypothesis Test for Paired Data |
| Are there more people living on the east side of creeks than the west side? 300 creeks were investigated. | Hypothesis Test for Paired Data |
| Is the flu shot effective? 1000 people who were given the flu shot and 2000 who were not were asked six months later if they got the flu over the past six months. | Hypothesis Test for the Difference Between 2 Proportions |
| Are men more likely to smoke cigarettes than women? 90 men and 90 women were questioned. | Hypothesis Test for the Difference Between 2 Proportions |
| Are dogs more likely than cats to leave the room when they are scolded for doing something wrong? 87 dogs and 42 cats were observed as they were scolded. | Hypothesis Test for the Difference Between 2 Proportions |
| Does holding on to a crystal improve psychic ability? 5000 people were each asked to guess the outcome of a coin toss first without the crystal and then while holding the crystal. | Hypothesis Test for the Difference Between 2 Proportions |
| Are people more likely to die of heart disease or cancer? 20,000 death certificates were examined. | Hypothesis Test for the Difference Between 2 Proportions |
| Does it rain more often on the west coast than on the east coast? 200 days were observed. | Hypothesis Test for the Difference Between 2 Proportions |
| Are unemployed people more likely to commit a felony than employed people? 5000 unemployed and 20,000 employed people were observed for a year. | Hypothesis Test for the Difference Between 2 Proportions |
| Does the general public respect politicians more after an election than before? 500 people were asked if they respected politicians before the election and then after the election. | Hypothesis Test for the Difference Between 2 Proportions |
| Do left-handed people have a higher tendency to enter careers in health care than right-handed people? 400 lefties and 300 right-handed people were questioned. | Hypothesis Test for the Difference Between 2 Proportions |
| Do bears that raid trash cans in the Tahoe Basin have a higher rate of survival over a one-year period than bears that do not raid trash cans? 34 bears that raided trash cans and 34 that did not raid trash cans were observed. | Hypothesis Test for the Difference Between 2 Proportions |
| The percent of people of each blood type in America is well known. A researcher wants to see if these percentages are different for the Amish population. | Chi-Square Goodness of Fit Test |
| Is the average commute time to work the same for all counties in California? 4000 workers from all over California were asked what county they were born in and how long it took them to commute to work. The statewide average commute is 27 minutes. | Chi-Square Goodness of Fit Test |
| Does the parking lot have the same number of cars each weekday? Cars were tallied Monday, Tuesday, Wednesday, Thursday, and Friday. | Chi-Square Goodness of Fit Test |
| A realty firm is interested in whether there are certain days of the month that are more likely than others for selling a house. Data was taken over the last several years. | Chi-Square Goodness of Fit Test |
| Do statistics students follow the same distribution of college majors as the rest of the college? 45 students were queried. | Chi-Square Goodness of Fit Test |
| Do all working hours experience the same productivity levels? 1000 employees were observed during each of the eight hours from 9:00 to 5:00. | Chi-Square Goodness of Fit Test |
| Are some times at which classes are offered more popular than others? Seven sections of the same math classes were offered and enrollments of each were tabulated. | Chi-Square Goodness of Fit Test |
| Do residents from each state spend the same amount of time on average watching television? 8000 people were asked what state they were born in and how many hours per week they watch television. The national television-viewing rate is 16 hours per week. | Chi-Square Goodness of Fit Test |
| Is the distribution of ages at a university normally distributed? Counts were taken of students within one, two, and three standard deviations from the mean. | Chi-Square Goodness of Fit Test |
| Is the dealer at the blackjack table cheating? The gaming commission tracked what cards the dealer gave himself for 3000 different black jack hands. | Chi-Square Goodness of Fit Test |
| Does knowing a student’s transfer goals help us to predict what letter grade that student will get in their statistics class? 3000 students were asked if they intended to transfer to a CSU, UC, UNR, or other university and then their grades were recorded. | Chi-Square Test for Independence |
| Is hair color related to what people do in their free time? 5000 people were questioned. | Chi-Square Test for Independence |
| Is there an association between dog breeds and the type of job the dog's owner has. 5,000 dogs were investigated. | Chi-Square Test for Independence |
| Does knowing which country a person’s maternal grandmother was born help predict that person’s political affiliation? 4000 people were asked what country their maternal grandmother was born in and what their political affiliation is. | Chi-Square Test for Independence |
| Is blood type related to astrological signs? 3000 people were surveyed. | Chi-Square Test for Independence |
| Is political affiliation related to the month that the person was born in? 3000 voters were studied. | Chi-Square Test for Independence |
| Is the type of dog a person owns a predictor of personality type?5000 people were part of a survey. | Chi-Square Test for Independence |
| Is hair color related to what people do in their free time? 5000 people were questioned. | Chi-Square Test for Independence |
| Does knowing what type of living arrangement (hours, apartment, dorm, other) help predict a student’s major (science, humanities, language, other)? Six-hundred students were questioned about their living arrangement and their major. | Chi-Square Test for Independence |
| Is race a predictor of political affiliation? 2000 people were surveyed about their race and political affiliation. | Chi-Square Test for Independence |
| Have shoe brand preferences changed between last year and this year? 1000 people were observed this year and 500 last year to see what brand of shoe they were wearing. | Chi-Square Test for Homogeneity |
| Do colors of shirts and colors of pants occur at the same frequency? 300 people were observed for the primary color of their pants and 300 others were observed for the primary color of their shirt. | Chi-Square Test for Homogeneity |
| Is the distribution of majors the same for LTCC students as it is for TMCC students? 1800 LTCC students and 2600 TMCC students were surveyed. | Chi-Square Test for Homogeneity |
| Do people on computers and people on handhelds use the same Internet search engines. 1000 web searches from a computer and 1500 web searches from a handheld were tracked to see what search engine was used. | Chi-Square Test for Homogeneity |
| Is the distribution of bird species in the Tahoe area the same as in the Yosemite area? 720 Tahoe area birds and 814 Yosemite area birds were observed. | Chi-Square Test for Homogeneity |
| Is the distribution of people’s favorite color different from the distribution of the color of clothes that they wear? 950 people were asked what their favorite color was and 500 were observed for the primary color worn. | Chi-Square Test for Homogeneity |
| Are living conditions (dorm, condo, apartment, with parents, etc.) different for Northern California college students compared to Southern California college students? 1400 Northern California and 1700 Southern California college students were questioned. | Chi-Square Test for Homogeneity |
| Do men and women watch different television shows? 780 men and 650 women who watched TV on Wednesday at 8:00 PM were asked what show they watched. | Chi-Square Test for Homogeneity |
| Does the cause of death for wealthy people follow a different distribution from the cause of death for poor people? Death certificates for 1500 wealthy people and 2500 poor people were looked at. | Chi-Square Test for Homogeneity |
| Is the distribution of sports that people play different from the distribution of sports people watch? 800 people were asked what sport they most often played and 800 others were asked what sport they most often watched. | Chi-Square Test for Homogeneity |
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