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Chapter 3 Linear Motion Hang Time Some athletes and dancers have great jumping ability. When leaping, they seem to momentarily "hang in the air" and defy gravity. The time that a jumper is airborne with feet off the ground is called hang time. Ask your friends to estimate the hang time of the great jumpers. They may say 2 or 3 seconds. But surprisingly, the hang time of the greatest jumpers is almost always less than 1 second! A longer time is one of many illusions we have about nature. To better understand this, find the answers to the following questions: 1. If you step off a table and it takes one-half second to reach the floor, what will be the speed when you meet the floor? 2. What will be your average speed of fall? 3. What will be the distance of fall? 4. So how high is the surface of the table above the floor? Jumping ability is best measured by a standing vertical jump. Stand facing a wall with feet flat on the floor and arms extended upward. Make a mark on the wall at the top of your reach. Then make your jump and at the peak make another mark. The distance between these two marks measures your vertical leap. If it's more than 0.6 meters (2 feet), you're exceptional. 5. What is your vertical jumping distance? 6. Calculate your personal hang time using the formula d = 1/2 gt². (Remember that hang time is the time that you move upward + the time you return downward.)
Sri K.
Gators have shown the ability to determine the direction of airborne sound. But can they locate underwater sounds? This was the subject of a study. Alligators were monitored for movement toward a sound produced from a submerged diving bell. Movements within 180° of the direction toward the sound were recorded as movements toward the sound. Movements in other directions were scored as movements away from the sound. Consequently, the researchers assumed that the proportion of movements toward the sound expected by chance is 180°/360° = 0.5. In a sample of n = 100 alligators, 75 moved toward the underwater sound. Complete parts a through e below. Give the null and alternative hypotheses for testing whether the true proportion of alligators that move toward the underwater sound is higher than expected by chance. Let p be the true proportion of alligators that move toward the underwater sound. Choose the correct answer below. A. H0: p = 0.50 vs. Ha: p < 0.50 B. H0: p > 0.50 vs. Ha: p = 0.50 C. H0: p ≠ 0.50 vs. Ha: p = 0.50 D. H0: p = 0.50 vs. Ha: p ≠ 0.50 E. H0: p < 0.50 vs. Ha: p = 0.50 F. H0: p = 0.50 vs. Ha: p > 0.50 In a sample of n = 100 alligators, assume that 75 moved toward the underwater sound. Use this information to compute an estimate of the true proportion of alligators that move toward the underwater sound. (Round to two decimal places as needed.) Compute the test statistic for this study. (Round to two decimal places as needed.) Compute the observed significance level (p-value) of the test. (Round to three decimal places as needed.) Make the appropriate conclusion in the words of the problem. Test using α = 0.05.
Madhur L.
FLOW SHEET Not every test you will learn to do is used for all organisms. For example, virtually all Gram positive bacteria give the same result on Simmons Citrate agar, so there would be no reason to run that test once you know an organism is Gram positive. However, Simmons Citrate is a very helpful test for distinguishing between Gram negative organisms. You do not know in advance if your unknown will be Gram negative or Gram positive, so you will need to learn how to do all the tests. The first test you will do on the unknown is a Gram stain. If the culture is Gram positive, you will NOT want to bother running a Simmons Citrate. Likewise there are other tests that are useful only for certain groups of bacteria. Rather than run every test on your unknown, you need to write up a plan for what tests will make the best use of your time. This will make identifying your unknown much simpler and faster. This plan is called a flow sheet. It is an outline of the steps you will use to identify any unknown. For example, the flow sheet should start with a Gram stain. This will divide all possible bacteria into four separate groups (- rods, + rods, - cocci and + cocci). Just the Gram stain will tell you which of the four groups your unknown is in. Then you can run the tests that make sense for that group of bacteria. With nothing but the Gram stain, you will be able to eliminate more than half of the list of possibilities. Then you will use appropriate other tests to continue eliminating choices until there is only one possible organism. You must make a flow sheet for all four possible Gram reactions. You will have time during lab to work on your flow sheets, so if you are unsure or confused, you should get help. The flow sheet should include only the tests we have actually done in class. Some groups of bacteria are not represented in our collection of unknowns. There is no point in running tests for organisms we do not have. Remember your unknown will be one of the organisms we have worked with in the lab. You may or may not get the same unknown as someone else in your class. YOU MUST HAVE YOUR FLOW SHEET APPROVED BY YOUR INSTRUCTOR BEFORE YOU WILL BE ASSIGNED AN UNKNOWN. When you are assigned your unknown organism, you will start by doing a Gram stain. Once you are sure of the Gram reaction of your unknown, you must follow the steps on your flow sheet. As you move through the tests on your flow sheets, you must request the media you will need. Your instructor will check your flow sheets to be sure the media you request are on your flow sheet. YOU MAY NOT HAVE ANY MEDIA FOR TESTING YOUR UNKNOWN EXCEPT WHAT IS CALLED FOR IN YOUR FLOW SHEET. *Be very sure the Gram stain is correct, or you will be conducting the wrong tests. *Make sure you keep your unknown pure and uncontaminated. *Be sure your culture is alive and is growing well as you test. *Be cautious rather than trying to rush through tests. Hurry leads to contamination and poor results. It takes less time to do each test once carefully than to have to repeat tests that are ambiguous or contaminated.
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The Practice of Statistics for AP
Introductory Statistics
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