Tom wants to know how long (in minutes) it takes to walk from the State Library to the Peter Hall Building. Over the past ten days, Tom records the time (in minutes) needed for him to finish the trip, as follows: 12.1 12.2 17.4 13.1 17.8 19.8 13.0 10.8 18.4 16.0 Assuming a normal distribution N(µX, σ2 X) for these observations, please answer the following: (a) If σX is unknown, calculate a 95% confidence interval for the mean. (b) Assume σX = 3 minutes and that you want a 95% confidence interval of width 2 (i.e. ±1). How many experiments are needed? 1 Tom also has a record, from a month ago, of the time for him to walk from Queen Victoria Market to the Peter Hall Bulding, as follows: 20.1 21.3 20.4 21.7 20.3 19.5 19.4 19.9 Assuming a normal distribution N(µY , σ2 Y ) for these observations, please answer the following: (c) Calculate a 95% confidence interval for µX − µY . (d) Calculate a 95% confidence interval for σ 2 X/σ2 Y . (e) (R) Calculate a 95% confidence interval for σ 2 X/σ2 Y , using the R function var.test()
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!
Tom wants to know how long (in minutes) it takes to walk from the State Library to the Peter Hall Building. Over the past ten days, Tom records the time (in minutes) needed for him to finish the trip, as follows: 12.1 12.2 17.4 13.1 17.8 19.8 13.0 10.8 18.4 16.0 Assuming a
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