Section 1 Lab Activity (2)

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3090

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Apr 3, 2024

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STAT 3090 S ECTIO N 1 L AB A CTIVITY S PRI N G 2024 N AME : P URPOSE : Some of the first questions we need to ask ourselves when confronted with interpreting data are “Who or what is this data about?”, “Where did this data come from?”, What kind of data am I looking at?”. These initial questions will help us determine how to analyze and interpret the data. The following activity will help us practice answering these questions using the language specific to statistics. O BJECTIVES : Upon successful completion of this assignment, you will be able to… • Classify data into data types • Identify the population, sample, parameter, statistic in context • Determine if a statistic is being used for inference • Determine the type of study from the context of a problem • Distinguish between explanatory and response variables 1. Sleepy Hollow (40 pts) The town of Sleepy Hollow has 18,000 residents over the age of 10. We have recorded for us the number of hours generally slept per night by each resident over the age of 10. You will find this data by going to the website: https://www.rossmanchance.com/applets/2021/sampling/OneSample.html Be sure that the population data is for “Sleep 1”. Also, select “Show Sampling Options” on the right side. Realistically, it would be very difficult to record data for every person in this town. Thus, we would likely take a sample of the residents, calculate statistics from the sample data, and use those statistics as an educated guess for the actual population parameters of interest. We will use this data set to draw a sample of size 9 to illustrate several concepts of populations, samples and data. a. What is the population? (4 pts) residents over the age of 10 1

STAT 3090 S ECTIO N 1 L AB A CTIVITY S PRI N G 2024 b. Define at least two parameters that could be calculated from this population data. (4 pts) The true number of hours of sleep from residents over 10 The mean of hours of sleep from residents over 10 c. What is the value of the population mean (average)? Include units with your answer. (4 pts) 8.001 skins d. Is the value you listed in part c a parameter or a statistic? Explain. (4 pts) Parameter e. Take one sample of size 9. (4 pts) Under Sampling Options set the N umber of samples to 1 and the Sample size to 9. Select Draw Samples . Record below the data values for your sample. Observation Value 1 8.75 2 5.75 3 6.75 4 8.25 5 11.50 6 8.25 7 7.75 8 9.25 9 5 2

STAT 3090 S ECTIO N 1 L AB A CTIVITY S PRI N G 2024 f. What is the value of your sample mean? Include units. (4 pts) 7.917 hours g. Explain why the value calculated in part f is a statistic. (4 pts) Its a mean value from a sample not the entire population h. Use the table below to report the mean from 5 of your classmates. (4 pts) i. Compare your mean to that of your classmates. Are the values the same of different? Why? (4 pts) Values are different because each sample contains different elements from the population since it was randomly chosen j. The mean you found for your sample is an example of a descriptive statistic. How could you use this value for inference? (4 pts) You can use to mean to find a general estimation for the rest of sleepy hollow Classmate Name: Mean Demetri 7.222 Zachary 7.111 Dominic 8.028 Ava 8.944 Chris 7.083 3

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STAT 3090 S ECTIO N 1 L AB A CTIVITY S PRI N G 2024 2. Stressed Out (21 pts) Because of concerns about employee stress, a large company is conducting a study to compare two programs (tai chi or yoga) that may help employees reduce their stress levels. Tai chi is a 1200-year-old practice, originating in China, that consists of slow, fluid movements. Yoga is a practice, originating in India, that consists of breathing exercises and movements designed to stretch and relax muscles. The company has assembled a group of volunteer employees to participate in the study during the first half of their lunch hour each day for a 10-week period. Each volunteer will be assigned at random to one of the two programs. Volunteers will have their stress levels measured just before the beginning of the program and ten weeks later at the completion of it. The difference in the two stress levels will be recorded. a. Identify the explanatory and response variables in the following study. Use a sentence or two to explain your choices. (7 pts) Explanatory Variable Program assigned Response Variable Stress level b. Would this study be considered an experiment or an observational study? Explain. (7 pts) Experiment because they are being assigned a program which means they are a control group in an experiment c. How could you perform this study so that it is the other method from the one you selected in part b? (7 pts) Allow the people to choose which program they want to be in 4

STAT 3090 S ECTIO N 1 L AB A CTIVITY S PRI N G 2024 3. Complete in WebAssign the Section 1 assignment. (39 pts) 5

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