t is known the population IQ score follows a normal distribution with mean as 100, SD as 10. A researcher is interested in studying if the average IQ of students from statistics courses on average has a higher IQ score than the population IQ score. To test this hypothesis, the researcher randomly collected a sample of 25 students from statistic class, the mean IQ score for this sample is 110. Compete for the hypothesis test at 1% significant level.
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!
It is known the population IQ score follows a
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