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Day 1
1. In 2013, 46% of employed Americans said that basic mathematical skills were necessary for their job. A researcher wants to know if the rise in technology has caused that number to increase. In a random sample of 150 employed Americans, 87 reported that basic mathematics was necessary for their job.
2. A Wisconsin high school wanted to know if their students were prepared enough to take the SAT. They wanted to know if there was evidence that their students performed worse on average than the national average of 66% of the possible 1600 points. They sampled 50 random students' scores and found they had an average of 63% with a standard deviation of 6.6 percentage points.
3. Two neighboring school districts are being compared in a study. Parents of children who go to each school were randomly sampled and asked if they were satisfied with their child's education. In District A, 145 out of 276 parents stated that they were satisfied. In District B, 198 out of 389 parents said they were satisfied. Is there evidence that there is a difference between the two districts in parents’ satisfaction with their children’s education?
4. A researcher wants to find the relationship between the number of pages per book and the number of words in the book.
Is there evidence that the number of words is correlated with the number of pages?
5. A large office building wants to decide between two brands of printers. To decide, they want to know which printer can go longer without having to replace the ink. They buy one of each of the potential printers, print paper until each printer runs out of ink and record the number of pages printed. Then they replace the ink and repeat this process 5 more times. The 6 observations of each can be shown on the Normal Probability Plots below. Printer A’s average was 2,234 pages with a standard deviation of 56.7 pages. Printer B’s average was 1,984 with a standard deviation of 103.4 pages.
Printer A Printer B
6. A lumberyard is worried that one of its saws is not cutting consistently. They advertise that their 2x4 boards have a mean width of 4 inches with a standard deviation of no more than .025 inches. They conduct a sample of 100 boards cut by the saw to find that the sample standard deviation is .029 inches. Is there evidence that the standard deviation of the population is greater than .025 inches?
7. A certain brand of apple juice is sold in 64.0 ounce bottles. The company wanted to make sure that the average amount in each bottle was correct. They sampled 245 random bottles of juice and found an average of 64.02 ounces with a standard deviation of 0.003 ounces. Is there evidence that the bottling machine does not fill the bottles to an average of 64 ounces?
8. UWEC wanted to know if the average amount of sleep that students get each night is associated with the year of the student. The distribution of sleep time does not follow a normal distribution. The surveyed 55 first-year students and 55 seniors. On average, the first-year students reported that they got 7.3 hours of sleep each night with a standard deviation of 2.34. The seniors’ average was 6.3 hours with a standard deviation of 3.6 hours. Is there evidence students’ year in school is associated with how much sleep they get?
9. A newspaper claims that 1/3 of coffee shop patrons only go to one coffee shop consistently. A local coffee shop wonders if their shop is above average, so the owner surveys 23 customers. 8 customers say they only get coffee there. Is there evidence that the local coffee shop’s proportion is higher?
10. In a blind taste test, people were given one can of either Coca-Cola or Pepsi brand soda, and asked whether they enjoyed it. 55% of 100 people said they enjoyed their can of Coca-Cola and 68.2% of 110 people said they enjoyed their can of Pepsi. Is there evidence that people enjoy Pepsi more often than Coca-Cola?
11. Rutgers University wanted to know if students’ living situation was associated with whether they drink alcohol. They surveyed 208 students and found the data shown in the table below.
Day 2
1. In 1990, the average amount of calcium in rainwater was 0.11 milligrams per liter. In 2010, another study found that there was an average of 0.17 milligrams per liter with a standard deviation of 0.03 milligrams per liter. The normal probability plot of the 7 data points is shown here. Is there evidence that the average increased from 1990 to 2010?
2. In a board game, players spin a spinner to pick a random number: 1, 2, 3, 4, or 5. Each number should be equally likely. To test this, the game manufacturer spins it 1000 times and records the outcomes. The outcomes were as follows:
Is there evidence that this spinner’s outcomes are not evenly distributed?
3. A company wants to know if its engineers and salespeople are equally likely to be satisfied with their jobs. They survey 40 random engineers and 30 random salespeople. 33 of the engineers and 19 of the salespeople said they were satisfied with their job. Is there evidence that an employee’s type of job is associated with their chance of being satisfied?
4. A previous study showed that 38% of families with children under the age of 18 ate dinner as a family at least 6 nights a week. A school board wants to know if this is true for their school district. They randomly sampled 48 families and found that 43.75% ate dinner as a family at least 6 nights a week.
5. Two programmers are comparing the speed of two algorithms they developed. They want to know if they run at different speeds on average. To test this, they each run their algorithm 50 times with random data and record the time it takes to run. It can be assumed that the distribution of run times is approximately normal. Algorithm A takes an average of 22.43 seconds with a standard deviation of 6.78 seconds. Algorithm B takes an average of 26.43 seconds with a standard deviation of 2.15 seconds. Is there evidence that the algorithms take different average amounts of time to run?
6. A research lab wants to test if there is difference in driving ability for drivers who are: driving normally, driving while talking on the phone, driving while texting, and driving while using a map. They do this by dividing the 100 test subjects into 4 groups randomly and assigning them to one of the four driving methods. Each subject drives through the test course and is given a score based on their performance. A summary of the scores is shown below. Is there evidence that a driver’s activity is associated with their performance?
7. A supermarket has two locations in the same town. Recent profit reports have shown that store A has a higher profit than store B. They theorize that the reason is the mean number of customers at store A is higher. For each store, they randomly select 7 days, and count how many customers are in the store at noon on those days. They find that store A had a mean of 39.6 customers with a standard deviation of 5.8, and store B had a mean of 19.4 with a standard deviation of 4.6. The normal probability plots for location A and location B are shown here. Is there evidence that store A has a higher mean number of customers (at noon)?
8. The national average of miles on a used car is 12,254. A used car dealership wants to know if their cars have a different average. So, they sample 8 used cars in their lot and find an average of 10,346 and a standard deviation of 1,204 miles. The normal probability plot is shown here. Is there evidence that the dealership has a different mean than the national average?
9. According to the U.S. Census Bureau, 7.8% of Americans have a travel time to work of more than 60 minutes. The city of Madison is concerned that this proportion is higher in their city. To decide if they need to update their public transportation system, they sample 1245 people who work in Madison. 9.8% of people claim that they have a travel time of more than 60 minutes.
10. A new drug has the potential to help treat acid reflex symptoms. 243 test subjects were randomly split into 2 groups: a test group and a placebo group. The placebo group had 121 members, and 32 of them said the pill helped with their acid reflex symptoms. The test group who were given the new medicine had 122 test subjects, and 76 of them said that the pill helped with their acid reflex. Can we claim that the new medicine works better than a placebo?
11. A town wants to know if the water quality is typically higher in the north part of town, compared to the south part of town. To do so, they sample the water supply of 5 random water pumps north and south of the town’s river and ranked their quality, with the best quality as 1 and the worst as 10. The ranks given to each pump are shown below:
Location
Ranks
North
1, 2, 4, 5.5, 9
South
3, 5.5, 7, 8, 10
Is there evidence that the median water quality is higher in the north part of town than in the south part of town?
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