STAT Lab Activity #1 (3)

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Clemson University *

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3090

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Statistics

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Feb 20, 2024

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N AME : Katie Hudson 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) All 18,000 Residents b. Define at least two parameters that could be calculated from this population data. (4 pts)

Average hours of sleep, standard deviation c. What is the value of the population mean (average)? Include units with your answer. (4 pts) 8.001 hours of sleep per night for residents over the age of 10 d. Is the value you listed in part c a parameter or a statistic? Explain. (4 pts) Parameter, because we used the whole population e. Take one sample of size 9. (4 pts) Under Sampling Options set the Number of samples to 1 and the Sample size to 9. Select Draw Samples . Record below the data values for your sample. Observation Value 1 7.500 2 8.139 3 8.611 4 7.944 5 8.333 6 7.917 7 7.722 8 7.889 9 9.167 f. What is the value of your sample mean? Include units. (4 pts) 8.136 hours of sleep per night for residents over the age of 10 g. Explain why the value calculated in part f is a statistic. (4 pts) Statistic, because you are only using a sample size of 9 rather than 18,000.

h. Use the table below to report the mean from 5 of your classmates. (4 pts) Classmate Name: Mean Andrew 7.888 Hugh 7.861 Zach 7.888 John 8 Connor 8.861 i. Compare your mean to that of your classmates. Are the values the same or different? Why? (4 pts) Different, because everyone had 9 different people in there sample 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 could infer that the parameter be similar to your descriptive statistic because you used samples found in the same pool, but it would not be the exact same because it is on a much smaller scale. 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.

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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 Whether they were assigned to yoga or tai chi Response Variable Stress levels b. Would this study be considered an experiment or an observational study? Explain. (7 pts) Experimental, because the element of control makes it 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) Let the sample group choose whether they would prefer yoga or tai chi. 3. Complete in WebAssign the Section 1 assignment. (39 pts)

STAT Lab Activity #1 (3)

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