An obstacle course was set up on a campus , and 11 volunteers were given a chance to complete it while they were being timed. They then sampled a new energy drink and were given the opportunity to run the course again. The "Before" and "after" times in seconds are shown below. Is there sufficient evidence at a = 0.05 to conclude that the students did better the second time? Assume the variables are normally distributed. (Consider the difference D= Before - After) Before 68 76 81 75 77 67 72 72 70 78 82 After 70 73 76 68 73 68 70 76 65 75 78 a) State the hypotheses and identify the claim with the correct hypothesis. 01. Ho:HD =0 Not claim H:Ho #0 claim 02. Ho:Ppz 0 Not claim H1:Hp <0 claim 03. Ho:Ho s0 Not claim H1:Po >0 claim
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

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