Rec 2 - SOLUTIONS

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Apr 3, 2024

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STAT 1430 Recitation 2A SOLUTIONS Part 1: Experiments Suppose we want to study and compare the volume of popcorn produced by two brands of microwave popcorn. We will take 30 bags of popcorn of brand A and 30 bags of brand B and cook them various amounts of time in a random order in the same microwave. At the end, the volume of popcorn produced will be measured and recorded. 1. What is the factor (independent variable) in this experiment? a. Brand of popcorn b. Cooking time c. Volume of popcorn produced d. None of the above 2. What is the response (dependent variable) in this experiment? a. Brand of popcorn b. Cooking time c. Volume of popcorn produced d. None of the above 3. What could be a confounding variable in this experiment? (The definition is in your notes if you need it.) List one and justify. Any reasonable answer is okay EXCEPT the factor or response variables. Examples include cooking time, temperature, weight of bag, time between trials, etc. 4. What other conditions do you think would need to be controlled in order for this to be a good experiment? Many possible answers here, one huge one being how long each bag of popcorn is popped. Do you use the same amount of time for each bag? Or do you use the directions on the bag and pop until there are 2 seconds between pops? You might also think about the condition of the microwave – is it reliable? Does it heat evenly and consistently? Also, consider the age of the bags of popcorn to make sure some have not expired. 5. The personnel director at a large company studied the eating habits of the company’s employees. The director noted whether employees brought their own lunches to work, ate at the company cafeteria, or went out to lunch. The goal of the study was to improve the food service at the company cafeteria. What type of study is this? a. Observational study b. Experiment 6. A doctor collects data on 200 of her patients who come in every year for their annual physicals. After 10 years, she compares the health status of the smokers to nonsmokers. What type of study is this? a. Observational study

STAT 1430 Recitation 2A SOLUTIONS b. Experiment 7. To help students perform better on the SAT, a private organization develops a study guide. To see if the guide is effective, they randomly sample 100 students: 50 students are randomly chosen to use the study guide, and the other 50 do not. At the end of the study, the SAT score is recorded. What is the response variable? a. Study guide: yes or no b. SAT score c. The sample of 100 students 8. To see if aspirin reduces the rate of heart attacks, a drug researcher randomly samples a total of 40 people. They randomly assign 20 people to take an aspirin each day and 20 people to take a fake pill each day. Then after a year they look to see whether or not each person had a heart attack during that year. They explore the data to see if there is a relationship between taking aspirin and having a heart attack. This is an: a. Observational study b. Experiment 9. According to our lecture notes, a well-designed experiment has which of the following 3 characteristics? Circle ALL that APPLY. a. Randomization of subjects to treatments b. Comparison of the results from different groups c. Plenty of confounding variables 10. Suppose you give 10 people a taste test where they each try samples of two different brands of soda. You randomize the order in which the soda samples are given to the participants. After drinking both samples they tell you which soda they liked best. What is a/the factor in this experiment? a. Number of participants b. Brands of soda c. The order in which the samples were given to the participants. d. Which soda the participant liked best. For the remaining problems in this section, use the following information: Bob wants to see if drinking caffeine in your water can keep you awake longer. He finds 60 volunteers for his study. He fills 120 stainless steel bottles with water. In half the bottles he places 48 milligrams of caffeine (about as much as in a Diet Coke). You cannot taste the caffeine. He randomly assigns 10 students to drink 1 bottle of regular water at 8pm; 10 students to drink 1 bottle of caffeinated water at 8pm; 10 students to drink 2 bottles of regular water at 8 and 9 pm; 10 students to drink 2 bottles of caffeinated water at 8 and 9 pm; 10 students to drink 3 bottles of regular water at 8pm, 9pm, and 10pm; and 10 students to drink 3 bottles of caffeinated water at 8, 9, and 10 pm. No one knows which subject got which treatment. He watches the volunteers and records the times that they fall asleep and compares the sleep times for all the groups.

STAT 1430 Recitation 2A SOLUTIONS 11. What is the independent variable in this study? Be careful. Whether or not they had caffeine in their water 12. How many treatment groups are there (count the control groups in this.) 6 groups 13. What is the response variable? Amount of time until they fell asleep 14. Evaluate this experiment in terms of the 3 criteria listed in your lecture notes: (List the criteria first, then give your opinion.) ONE: Makes Comparisons TWO: Avoids Bias THREE: Has enough data Answers for your opinion will vary, check with your TA if you have questions about your answer. 15. List at least one confounding variable in this study. Many possible answers, check with your TA if you have questions about your answer. Part 2: Organizing Data 1. In general, can you recreate the original data values from its histogram? a. Yes b. No 2. We know that if a histogram is skewed left, then the mean is less than the median. This is because: a. There are a few small values in the data set compared to the rest. b. There are a few large values in the data set compared to the rest. 3. Suppose an exam is 48 minutes long and most of the students stayed until the very end although there were a few students who finished early . You collect data on how much time each student spent taking the exam and make a histogram. The shape of the histogram will be what? (Hint: DRAW A PICTURE) a. Skewed left b. Skewed right c. Symmetric

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STAT 1430 Recitation 2A SOLUTIONS 4. Suppose you have a numerical data set that is very much skewed to the left. If you had to pick one, which measure of center best represents most of the data in this case? a. Mean b. Median 5. It is possible for the average of a data set to be larger than most of the values in that data set. a. True b. False 6. The mean of a data set must be one of the values in the data set. a. YES b. NO 7. The median of a data set must be one of the values in the data set. a. YES b. NO 8. The amount of time students take to finish a 2 hour exam shows that a lot of students wait until the very end to turn in their exams, while only a few finish early. Which shape is mostly likely to represent the exam times? a. Symmetric b. Skewed right c. Skewed left Next 2 problems: The amount withdrawn for each customer from a bank are recorded over a day’s time and summarized in the histogram below. 9. What is a better name for the Y-axis here? a. Number of Customers b. Amount of Money c. Number of Withdrawals 10. Two measures of center were calculated: 176 and 160. One of these numbers is the mean, and the other is the median. Which one is the median? a. 176 is the median b. 160 is the median c. Can’t tell

STAT 1430 Recitation 2A SOLUTIONS 11. Last year a small accounting firm paid each of its five clerks $25,000; two junior accountants received $60,000 each; and the firm’s owner got paid $255,000. This year the firm gave no raises to the clerks and the junior accountants, but the owner’s salary is increased to $455,000. How does this year’s raise affect the average salary for the accounting firm? a. The average salary for the firm will increase b. The average salary for the firm will decrease c. The average salary for the firm will stay the same Next 2 questions : The owner of a large fleet of taxis has recently converted his taxis to operate on propane instead of gasoline, due to the high cost of gasoline. He wants to know what the average miles per gallon (MPG) is for all of the taxis in his fleet under the new propane fuel system. He takes a random sample of taxis from his fleet, and calculates the miles per gallon for each taxi on propane. The results are shown below. Descriptive Statistics: Mileage Variable Count Mean StDev. Min. Q1 Median Q3 Max. Mileage 50 19.784 3.093 13.300 17.800 20.000 21.825 26.000 12. Why would you say the data must be close to symmetric? a. Because it is easier to interpret symmetric data b. Because the mean and median are close to each other c. Because the minimum and maximum are close together d. There is not enough information to determine that the data are close to symmetric

STAT 1430 Recitation 2A SOLUTIONS 13. Suppose after taking the sample, the owner notices that the next taxi in his fleet gets 35 miles per gallon. Which of the following statistics will be the least affected by adding this taxi to the data set? a. The mean b. The median c. The maximum d. All of these will be affected the same amount 14. Which of the following data sets has more variability around the mean, the first or the second? a. b. Next 3 questions: refer to the histogram below, describing the amount of time required to answer questions on a telephone support line. There were 300 calls altogether. Histogram 0 10 20 30 40 50 60 70 80 90 100 -2 2 6 10 14 18 22 26 30 34 38 42 More Frequency

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STAT 1430 Recitation 2A SOLUTIONS 15. The number of calls that last more than 18 minutes is approximately: (Look carefully at the end points of the bins!) a. 10 b. 30 c. 22 d. 100 16. The shape of the data set is a. skewed right b. skewed left c. symmetric 17. The median of this dataset is: (choose best answer) a. 18 b. 5 c. 12 d. 14 18. OSU wanted to research how much money students spent on textbooks each semester. From a random sample of 200 students, they found that the average amount spent on textbooks for a semester is $300 and the distribution is skewed right. This indicates that: a. The median amount spent on textbooks would be greater than $300. b. The median amount spent on textbooks would be less than $300. c. The median amount spent on textbooks would be $300.

Rec 2 - SOLUTIONS

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