Calculating and interpreting the t test statistic: (a) Let's say µ = 19. A sample of size 13 obtained the sample mean x = 25 and the sample standard deviation s = 6. Find P (x > 25). (b) Assume that researchers regard a probability smaller than 5% small. Since P(x > 25) is %3D to have than 5%, it is obtained such a sample mean. In other words, provided the population mean of 19, a sample mean this far from the population mean is highly unlikely to occur by pure chance alone. To put it in another way, the fact that this sample mean of 25 occurred cast doubt on the validity of the assumption of 19. a. larger; surprising; does b. larger; not surprising; does not c. smaller; surprising; does d. smaller; not surprising; does not
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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