Confidence Interval for a Population Mean

Confidence Interval for a Proportion

Confidence Interval for the Diff. Between 2 Means (Independent Samples)

Confidence Interval for Paired Data (Dependent Samples)

Confidence Interval for the Difference Between 2 Proportions

Prediction for a Single Value of y for a Fixed x

Hypothesis Test for a Population Mean

Hypothesis Test for a Population Proportion

Hyp. Test for the Difference Between 2 Means (Independent Samples)

Hyp. Test for Paired Data (Dependent Samples)

Hyp. Test for the Difference Between 2 Proportions

Chi-Square Goodness of Fit Test

Chi-Square Test for Independence

Chi-Square Test for Homogeneity

Confidence Interval for a Population Mean

1. You ask 300 people how happy they feel on a scale from 1 to 100. Estimate the mean happiness.

2. What is the average loss for new businesses during their first year? 82 new businesses were tracked.

3. You are interested in estimating the average number of people individuals interact with each day. You survey 300 Americans.

Confidence Interval for a Proportion

1. A new method of packaging eggs is being tested. The manager is interested in estimating the proportion of eggs that will be broken upon delivery. A shipment of 3000 eggs was examined.

2. What proportion of all business owners inherited the business from their parents? 500 business owners were surveyed.

3. 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 the Diff. Between 2 Means (Independent Samples)

1. 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.

2. 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.

3. 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 Paired Data (Dependent Samples)

1. How much more money does the typical restaurant customer spend on the main course vs. the other items? 45 customers were observed.

2. How many fewer crimes will be committed in an area where policemen are patrolling? 50 locations were studied for the number of crimes committed before policemen were assigned to patrol the locations and after they began patrolling.

3. Seventy-four South Tahoe residents were asked how many cups of coffee they drank each week and how many glasses of water they drank each week. Estimate the mean difference between the average number of cups of coffee South Tahoe residents drink and the average number of glasses of water they drink.

Confidence Interval for the Difference Between 2 Proportions

Prediction for a Single Value of y for a Fixed x

1. A study was done to see how much gas Americans consume. 600 Americans were asked how far they lived from their work and how many gallons of gas they used each week. Find a confidence interval for the mean amount of gas that is used by Americans who live 15 miles from work.

2. The Lake Tahoe Visitor Bureau has collected data on the number of patrons at Tahoe area restaurants on several days with various hotel vacancy rates in the area. Estimate the number of patrons at Tahoe area restaurants when the vacancy rate is 23%.

3. An atmospheric scientist is studying the relationship between global CO2 levels and global temperatures. He has data of CO2 levels vs. global temperatures and wants to predict the global temperature if the CO2 level becomes 290,000 ppb.

Hypothesis Test for a Population Mean

1. 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.

2. Will a light bulb last for more than 500 hours on average? 200 bulbs were observed.

3. Do cars average greater then 5 miles an hour over the speed limit? Police officers randomly clocked 850 cars.

Hypothesis Test for a Population Proportion

1. Are children of divorced parents more likely to call their father than their mother when they need to borrow money? 100 children of divorced parents were asked who they called last time they needed money.

2. Does the home team win the majority of the time? 100 games were observed.

Hyp. Test for the Difference Between 2 Means (Independent Samples)

1. Can chimps learn more words than apes? Biologists spent a year with eighty chimps and 80 apes teaching them vocabulary.

2. Do politicians who are democrats spend more time with lobbyists than do republican politicians? 35 democrats and 35 republicans took part in the survey.

3. 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.

Hyp. Test for Paired Data (Dependent Samples)

1. Does Kirkwood receive more snow on average than Squaw Valley? The snowfall at each result was measured at each resort for each of the last 25 snow storms.

2. 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.

3. Fifty married couples were asked on a scale from one to ten how they felt about restricting pornography on the Internet. Is there sufficient evidence to suggest that husbands agree to the restrictions more than wives?

Hyp. Test fro the Difference Between 2 Proportions

1. Is a man who walks into a car dealership more likely to purchase an automobile than a woman? 70 men and 60 women were observed.

2. 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.

3. Are robin eggs more likely then stellar jay eggs to hatch early during a wet spring? Eggs of 82 robins and 75 stellar jays were observed this spring.

Chi-Square Goodness of Fit Test

1. Are robin eggs more likely then stellar jay eggs to hatch early during a wet spring? Eggs of 82 robins and 75 stellar jays were observed this spring.

2. A stadium manager is interested in whether the fans that buy tickets are demographically the same as the general population of the city. Currently 42% are Caucasian, 35% are Hispanic, 12% are African American, 8% are Asian, and the rest are defined as other.

3. Do college students listen to the same radio stations as the general public? 2000 college students were asked what radio station they listened to. Their choices were compared to the known overall ratings.

Chi-Square Test for Independence

1. A police investigator is interested in finding a relationship between the weapon that is used for murder and the location where the murder occurs. 800 murder cases were examined.

2. Is the type of television show that a person chooses to watch related to the brand of deodorant that a person uses? 1500 people were surveyed.

3. Does knowing which main course a person orders help predict what desert that person will order? There are 9 main courses and 4 deserts on the dinner menu. 170 customers at your restaurant were observed.

Chi-Square Test for Homogeneity

1. Do Democrats and Republicans have the same phone carrier usages? 554 Democrats and 672 Republicans were asked what company they used for their phone service.

2. Is Gender a factor in a person’s favorite fruit? 400 men and 500 women were asked what their favorite fruit is to see if the distribution of favorite fruit is the same for men and women.

3. Do people on computers and people on hand helds use the same Internet search engines. 1000 web searches from a computer and 1500 web searches from a hand held were tracked to see what search engine was used.

Confidence Interval for a Population Mean

1. 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.

2. The school average on the statistics final is 78%. 45 students are assigned a computer supplement. Determine the confidence interval for the average score on the final for students who were assigned the supplement.

3. The school average on the statistics final is 78%. 45 students are assigned a computer supplement. Determine the confidence interval for the average score on the final for students who were assigned the supplement.

Confidence Interval for a Proportion

1. How likely are people who see a nickel on the ground to pick it up? 800 people were observed

2. A new method of packaging eggs is being tested. The manager is interested in estimating the proportion of eggs that will be broken upon delivery. A shipment of 3000 eggs was examined.

3. What percent of Tahoe residents have swam in the lake? 1008 residents were surveyed.

Confidence Interval for the Diff. Between 2 Means (Independent Samples)

1. 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.

2. 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.

3. How much longer will swimmers stay in a heated pool compared with an unheated pool? When the pool was heated 67 swimmers were observed and when the pool was unheated 55 swimmers were observed.

Confidence Interval for Paired Data (Dependent Samples)

1. How much does a speed reading course help. A word per minute read was charted before and after the course for 80 students.

2. 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.

3. 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 the Difference Between 2 Proportions

1. A medical researcher is studying the decline in the infection rate when a new surgery technique is used. 400 surgeries using the new technique and 400 using the old technique are performed and the patients are later checked to see if they developed an infection.

2. 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.

3. How much more likely is it for a person to own dog than a cat? 100 people were asked whether they own a dog and whether they own a cat.

Confidence Interval for Paired Data (Dependent Samples)

1. How much more money does the typical restaurant customer spend on the main course vs. the other items? 45 customers were observed.

2. 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.

3. 65 monkeys were part of an experiment where they each were placed in front of a computer for three hours to learn ten words. Then they were given a 3-hour lesson from a human to learn a different set of ten words. The number of successfully memorized words from the computer lesson and the number from the human lesson were recorded. How much more effective was the human lesson?

Hyp. Test for the Difference Between 2 Proportions

1. 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.

2. Are robin eggs more likely then stellar jay eggs to hatch early during a wet spring? Eggs of 82 robins and 75 stellar jays were observed this spring.

3. Are men more likely to stop their car and assist a woman with car troubles parked on the side of the road? 85 male drivers and 85 female drivers were observed.

Chi-Square Goodness of Fit Test

1. You suspect that a casino is using a Roulette wheel that is unfair. You observe the outcome of the wheel 900 times so see if each number is equally likely to be selected.

2. Does the political affiliation of congress reflect the known political affiliation of the American Public?

3. Does South Lake Tahoe have the same ethnic makeup as that of the (known) distribution of California? Five Hundred South Lake Tahoe residents were asked about their ethnicity.

Chi-Square Test for Independence

1. 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.

2. 5000 people were asked what their favorite movie is and who their favorite author is. Based on the data can you conclude that there is a relationship?

3. 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 Homogeneity

1. Is the racial distribution the same for UCLA and UCSD? 5000 students from each university were asked about their race.

2. Do Democrats and Republicans have the same phone carrier usages? 554 Democrats and 672 Republicans were asked what company they used for their phone service.

3. Are living condition (dorm, condo, apartment, with parents, etc.) different for Northern Californian college students compared to Southern Californian college students? 1400 Northern Californian and 1700 Southern Californian college students were questioned.