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Making the grade Here are a few lines from a statistics teacher’s grade book: What individuals does this data set describe?For each individual, what variables are given? Identify each variable as categorical or quantitative. Hotel choices A high school’s debate team is planning to go to Salt Lake City for a three-day competition. Team members will be responsible for sharing the cost of staying in a hotel for two nights. The competition’s sponsor provides a list of available hotels, along with some information about each hotel. Here is a chart that summarizes the hotel options. What individuals does this data set describe? Clearly identify each of the variables. Which are quantitative? If you were a debate team member, which hotel would you recommend? Why? Populations and samples, I For each of the following sampling situations, identify the population and the sample as exactly as possible. A furniture maker buys hardwood in large batches. The supplier is supposed to dry the wood before shipping (wood that is not dry won’t hold its size and shape). The furniture maker chooses five pieces of wood from each batch and tests their moisture content. If any piece exceeds 12% moisture content, the entire batch is sent back. An insurance company wants to monitor the quality of its procedures for handling loss claims from its auto insurance policyholders. Each month the company selects a sample from all auto insurance claims filed that month to examine the accuracy and promptness with which they were handled. Populations and samples, II For each of the following sampling situations, identify the population and the sample as exactly as possible. A business school researcher wants to know what factors affect the survival and success of small businesses. She selects a sample of 150 restaurants from those listed in the phone book for a large city. Your local television station wonders if its viewers would rather watch a local college basketball team play or an NBA game scheduled at the same time. It announces that it will show the NBA game and receives 89 calls asking that it show the local game instead. Bad Apples A truckload of apples arrives at an apple juice production plant. The plant’s quality control team selects three large buckets of apples from various locations within the truck. These apples are inspected carefully. Based on inspection results, the entire truckload is either accepted or rejected by the plant. Identify the population, sample, individuals, and variable(s) in this setting. 5391150698500J.K. Rowling’s Words Different types of writing can sometimes be distinguished by the lengths of the words used. A student interested in this fact wants to study the lengths of words used by J.K. Rowling in her Harry Potter books. She opens a Harry Potter book at random and records the lengths of the first 50 words on the page. What is the population in this study? What is the sample? What variable does the student measure? Tasty Muffins Before a new variety of frozen muffin is put on the market, it is subjected to extensive taste testing. People are asked to taste the new muffin and a competing brand and to say which they prefer. Is this an observational study or an experiment? Explain your answer. Cell phones and cancer One study of cell phones and the risks of brain cancer looked a group of 469 people who have brain cancer. The investigators matched each cancer patient with a person of the same sex, age, and race who did not have brain cancer, then asked about use of cell phones. Result: “Our data suggest that use of hand-held cellular telephones is not associated with the risk of brain cancer.” Is this an observational study or an experiment? Why?What individuals are measured, and what variables are recorded? Fit to lead? Is there a relationship between physical fitness and leadership ability? To answer this question, researchers recruit 100 students who are willing to take part in an exercise program. The volunteers are divided into a low-fitness group and a high-fitness group on the basis of a physical examination. All students then take a test designed to measure leadership, and the results for the two groups are compared.Is this an experiment or an observational study? Explain your answer. What population does it appear that the investigators were interested in? What variables did they measure?Explain why we might prefer a sample survey to using students who volunteer for a fitness program. Angry Bees My grandmother once told me that the color red makes bees angry. Here’s a method I’ve designed to test her claim. I’ll select half of my students (by drawing names from a hat) to wear red clothes and the other half to wear white clothes. Then I’ll turn a bunch of bees loose in our classroom and record how many times each student is stung. Is this an observational study or an experiment? Why? What variables are recorded? If students wearing red clothes are stung much more often than students wearing white, can we conclude that the color red causes bees to sting more? Why or why not? Comment on any flaws you see within my methods. ................
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