In the Northern Hemisphere, dolphins swim predominantly in a counterclockwise direction while sleeping. A group of researchers wanted to know whether the same was true for dolphins in the Southern Hemisphere. They watched eight sleeping dolphins and recorded the percentage of time that the dolphins swam clockwise. Assume that this is a random sample and that this variable has a normal distribution in the population. These data are as follows: 77.7, 84.8, 79.4, 84.0, 99.6, 93.6, 89.4, 97.2 What is the mean percentage of clockwise swimming for Southern Hemisphere dolphins? What is the 95% confidence interval for the mean time swimming clockwise in the Southern hemisphere dolphins? What is the 99% confidence interval for the mean time swimming clockwise in the Southern Hemisphere dolphins?
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!
In the Northern Hemisphere, dolphins swim predominantly in a counterclockwise direction while sleeping. A group of researchers wanted to know whether the same was true for dolphins in the Southern Hemisphere. They watched eight sleeping dolphins and recorded the percentage of time that the dolphins swam clockwise. Assume that this is a random sample and that this variable has a
77.7, 84.8, 79.4, 84.0, 99.6, 93.6, 89.4, 97.2
- What is the mean percentage of clockwise swimming for Southern Hemisphere dolphins?
- What is the 95% confidence interval for the mean time swimming clockwise in the Southern hemisphere dolphins?
- What is the 99% confidence interval for the mean time swimming clockwise in the Southern Hemisphere dolphins?
- What is the best estimate of the standard deviation of the percentage of clockwise swimming?
- What is the median of the percentage of clockwise swimming?
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